Gas Turbines

Gas Turbinesedited by Injeti Gurrappa SCIYO Gas Turbines Edited by Injeti Gurrappa Published by Sciyo Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2010 Sciyo All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by Sciyo, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Jelena Marusic Technical Editor Teodora Smiljanic Cover Designer Martina Sirotic Image Copyright Laurin Rinder 2010. Used under license from Shutterstock.com First published October 2010 Printed in India A free online edition of this book is available at www.sciyo.com Additional hard copies can be obtained from [email protected] Gas Turbines, Edited by Injeti Gurrappa p. cm. ISBN 978-953-307-146-6 SCIYO.COM WHERE KNOWLEDGE IS FREE free online editions of Sciyo Books, Journals and Videos can be found at www.sciyo.com Contents Preface IX 1 Chapter 1 Advances in Aerodynamic Design of Gas Turbines Compressors Ernesto Benini Chapter 2 Exergy and Environmental Considerations in Gas Turbine Technology and Applications Richard ‘Layi Fagbenle 29 65 Chapter 3 Design and Development of Smartcoatings for Gas Turbines I.Gurrappa and I.V.S. Yashwanth Chapter 4 Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 79 Zinfer R. Ismagilov, Mikhail A. Kerzhentsev, Svetlana A. Yashnik, Nadezhda V. Shikina, Andrei N. Zagoruiko, Valentin N. Parmon, Vladimir M. Zakharov, Boris I. Braynin and Oleg N. Favorski Chapter 5 Electricity Cogeneration using an Open Gas Turbine Anita Kovac Kralj Chapter 6 Gas Turbine Condition Monitoring and Diagnostics Igor Loboda 109 119 Chapter 7 Micro Gas Turbines 145 Flavio Caresana, Gabriele Comodi, Leonardo Pelagalli and Sandro Vagni Chapter 8 Gas Turbine Power Plant Modelling for Operation Training 169 Edgardo J. Roldán-Villasana, Yadira Mendoza-Alegría, Ma. Jesús Cardoso G., Victor M. Jiménez Sánchez and Rafael Cruz-Cruz Chapter 9 Life Prediction of Gas Turbine Materials Xijia Wu Chapter 10 Damage and Performance Assessment of Protective Coatings on Turbine Blades Jaroslav Pokluda and Marta Kianicová 215 283 VI Chapter 11 Application of Structural Analysis to Improve Fault Diagnosis in a Gas Turbine Cristina Verde and Marino Sánchez-Parra 307 Chapter 12 Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 325 Pavel Krukovsky, Konstantin Tadlya, Alexander Rybnikov, Natalya Mozhajskaya, Iosif Krukov and Vladislav Kolarik Chapter 13 Failure Investigation of Gas Turbine Generator Cooling Fan Blades by Experimental and Numerical Analysis 347 Ali Jahangiri . maintenance engineers and academicians such as the effect of environmental effects. 3. life prediction modeling and finally failure analysis of coatings and components. production of electricity cogeneration. they are now either out of date or fundamental in nature. design and development of smart protective coatings to provide total protection. The design and maintenance engineers in the gas turbine and aircraft industry will benefit immensely from the integration and system discussions in the book. The book comprises articles that bring out contemporary developments in gas turbines and thematically classified into the following categories: 1. 6.from advances in engine design and characterization for engineering design. maintaining them with maximum efficiency for more than a designed period but also the associated topics of life time modeling and failure investigations. There is a growing need to adopt advanced techniques / technologies to meet the ever increasing demand for high efficiency in existing engines and to develop modern gas turbines for strategic and special applications. various types of gas turbines. Several issues which are of interest to industry. the role of coatings for life time enhancement which in turn for increased efficiency. has been to fill this gap and provide recent developments not only in designing modern engines for a variety of applications. monitoring and assessment of turbines and coatings as well as related topics have been addressed in the book. 7. materials. therefore. maintenance. 2. The aim. turbine monitoring. 4. diagnostics. researchers and academia. The target audience for this book is design. This book is intended to provide valuable information for the analysis and design of various gas turbine engines for different applications. Although there have been a number of excellent books written on the subject. thus opening up the areas of challenge for designers. The contents provide useful feedback for further developments aimed at effective utilization of various types of gas turbines. researchers. 5.Preface During my experience of research for the last 25 years. aerospace and mechanical engineers. The chapters are of high relevance and interest to manufacturers. high temperature corrosion. ADVANCES IN DESIGNING GAS TURBINE COMPONENTS GAS TURBINE TECHNOLOGIES APPLICATIONS OF GAS TURBINES ENVIRONMENTAL EFFECTS COATINGS DEVELOPMENT AND THEIR APPLICATIONS MONITORING AND DISGNOSTICS LIFE PREDICTION The book commences with articles on advances in designing gas turbine engines and related technologies. This book covers a broad spectrum of chapters spanning the entire gas turbine and aerospace industry. I have felt the need for a text book written specifically for Design Engineers and Materials Scientists. researchers and academicians as well. . The editor thanks all the contributors for the rich technical content of the chapters based on their vast experience and expertise. Dr. Hence. Injeti Gurrappa Defence Metallurgical Research Laboratory Kanchanbagh PO. September 2010 Editor Prof. Hyderabad. In addition. failure investigations with advanced techniques and numerical analysis issues have also been addressed.X Life prediction of components and coatings is a very important aspect in gas turbines. the emphasis on life prediction modeling of materials and coatings has been described. India . Several articles focus on integrity of gas turbine components as well as damage and performance assessment. The editor also thanks the Sciyo Publishers for their timely efforts in the publication of this book. . . while experimental activity remains decisive for ultimate assessment of design choices. To this respect. where mathematical and statistical tools are implemented and used as a decisive support in the decision making process. is given. The compressor design still remains a very complex and multidisciplinary task. While traditional 1D and 2D design procedures are consolidated for preliminary calculations. along with Computational Fluid Dynamics (CFD) are assuming more and more importance for the detailed design and concrete evaluation of options. where aeromechanical. For this reason. In this perspective. axial-flow compressor design is always part of a more general framework involving the engine as a complex system.1 Advances in Aerodynamic Design of Gas Turbines Compressors University of Padova Italy 1. Choice of the design point In both stationary and aircraft medium-to-high size gas turbines. compressors are seen mainly as one of the engine components. a contribution to illustrating the roadmap for modern compressor design technique development. as well as an updated picture of available procedures. traditionally considered prevalent. specifically those carrying out the compression phase. due to the peculiar way in . technological. the complexity evidenced above claims for a more structured and organized way of handling the problem. now become part of a more general design approach. thus leading to a very challenging problem for designers. numerical design optimization techniques. designer experience still plays a decisive role. however. In this chapter. endwall contouring and casing treatments for enhanced stall margin and many others. noise-related concerns and many other matters have to be taken into account simultaneously. both conventional and advanced techniques will be presented and discussed. where aerothermodynamic issues. Introduction Aerodynamic design techniques of gas turbine compressors have dramatically changed in the last years. Ernesto Benini 2. such as new blade shapes for improved on-off design efficiency. structural. Nowadays. however. interesting and alternative options are in fact available for compressor 3D design. Starting from the precise formulation of the design problem and the choice of the so-called "design" or "nominal" condition. emerging techniques have been developed and are being used almost routinely within industries and academia. or at least the one chosen for the preliminary compressor sizing. today the engine is born closer and closer with the aircraft and its design is mainly driven by issues regarding thrust class and specific fuel consumption along some typical flight envelopes. whose design heavily affects the overall engine performance. compressors adopted in aircraft gas turbine engines. a condition representative for a real aircraft at departure. bur rather to change the air flow.e. In fact. Moreover. most of the interest is concentrated on the compressor design around the nominal condition. in off-design operations. Usually. i. since the gas turbine load is always kept as much constant as possible in order to preserve engine’s peak efficiency. compressors are perhaps the most crucial component to be designed. as the one where the engine runs at fixed point. technical objectives. especially at relevant points such as take-off and . In principle. rotational speed and pressure ratio derived from the cycle analysis at sea level ISA inlet conditions. load variations. the cycle analysis gives a unique combination for mass-flow rate. for instance direct operating costs and mean time between overhauls. In stationary gas turbines. when the compressor delivers almost a constant mass flow rate for a fixed shaft speed at the maximum possible efficiency. a goal which is pursued by changing the compressor stator vanes’ attitude. This in turn allows to clearly identify a cruise point. compressors are often regarded as “delicate” turbomachines. this occurs almost invariably for both single and multi-shaft engine configurations. Following this criteria. above all. Nowadays.e. when necessary. the nominal condition at which the compressor will operate most of the time is well defined and characterized by a unique combination of mass flow rate. in stationary gas turbines. the compressor design gives rise to a multi-point and multidisciplinary approach which should be able to incorporate off-design requirements into the design phase. both in design and. another reason rely on the fact that engine performance at fixed point are independent of the type of aircraft to which the engine is destined. compressor behaviour over the entire operating range. aeroengine manufactures rarely develop a new engine neglecting the type of aircraft it will joined with. such as specific thrust. Indeed. using inlet guide vanes (IGV) and/or variable stator vanes (VSV). some limiting constraints reduces the engine design space. often conflicting. rotational speed and compression ratio that make the basis for the preliminary design. As a result. e. which have to be traded-off and have a significant impact on the engine design. In such case. aeroengines are designed mainly to fulfil many. are implemented so as not to modify the thermodynamic cycle of the gas turbine. In many gas turbine designers’ opinion in fact. Among aeroengine compressor designers it is of common practice to define the nominal operating condition. when it develops a static thrust.g. In such cases.2 Gas Turbines which energy transfer occurs and the flow pattern which consequently establishes within them. particularly in civil applications. in particular standard ambient conditions and flight Mach number. range and fuel consumption within a wide range of flight conditions which typically require the engine to operate far away from its nominal conditions. from which compressor quantities can be derived. This because the fixed point operation can be easily characterized by experiments on a static test bench when a prototype of the designed engine will be available. require completely different design criteria (even though some stationary gas turbines are often derived and adapted from aeroengines to fulfil heavy-duty operation). at least from the aerodynamic point of view. often referred to as aeroengines. Corrections for nonstandard ISA operations can be accounted for at the early design phase when the engine is supposed to work far away from the sea level or under extreme temperature conditions. i. . which can be written in mathematical terms as follows: For given pa. can be accounted for only afterwards.xn)T and xi. and design (or decision) variables as follows: • Objectives: maximize adiabatic efficiency (η). other criteria must be accounted from the very beginning: these can derive either from other engineering requirements (structural.Advances in Aerodynamic Design of Gas Turbines Compressors 3 landing.n and n the number of decision variables. we shall make the assumption that. Structural. • Multi-disciplinary constraints: structural and vibrational. although not explicitly involved in the aerodynamic design. If not satisfactory. • Boundary conditions: inlet conditions (pressure pa. and above all compressor-turbine) as determined by a Matching Index (MI).x2. compressor and stage geometry parameters. technological and other constraints = g(X). (based on engine Power or Thrust requirements). mainly as a check. M. being X=(x1. costs. 3. correct compressorcomponent matching (i. in aeroengines) Maximize (η.. • Functional constraints: mass flow rate. compressor aerodynamic design is the procedure by which the compressor geometry is calculated which fulfils the design cycle requirements in the best possible way. technological.e. we can formulate the design problem by identifying objectives. manufacturability. constraints. constructive) or from non-technical aspects (mainly economical). Using a more definite statement. m. the designer iterates until well defined compressor characteristics are found at cruise conditions which satisfy all the constraints in the off-design one. reliability. more sophisticated design procedures attempt to identify the nominal condition by weighting some relevant compressor operating points along its operating line on the desirable map. To this respect.…. • Decision variables: number of stages. (from Cycle analysis). It is worth considering that. Aerodynamic design problem formulation Qualitatively speaking. the aerodynamic design of an axial-flow compressor is inherently a multiobjective constrained optimization problem. a nominal condition has already been defined using some criteria such that the compressor characteristics are known. IN fact. flight Mach number (in the case of an aeroengine). Pressure Ratio. compressor-combustor. Ta (and flight Mach number. boundary conditions. maximize stall margin (SM). • Side Constraints: each decision variables must be chosen within feasible lower and upper bounds (sides). intake-compressor. either within ground or onboard power plants. whatever the case in which the compressor will operate.. ….max for i=1.min< xi <xi. PR. temperature Ta). weight. both at nominal condition. In the following. accessibility. including both fixed point and cruise conditions. SM)= f(X) Subject to: m = m(X) PR = PR(X) Matching Index (MI) = MI(X) Cost function = Cost function(X) Weight. . On the other hand. a fact which ultimately affects the choice of the blade shape. From the problem formulations given above. a constraint based on the static thrust to be delivered by the overall engine at seal level is set which inevitably influences compressor design. technological and other constraints = g(X). i.e. in turn. will have an important impact on the choice of stage geometrical and functional variables. In another example. in a stationary gas turbine used for electric power generation. before examining how to deal with such problems. mainly depending on compressor’s final destination and/or manufacturer’s strategies. This. Ta Maximize (η. For example. In this case. while cost function is inevitably different to the one assigned to the civil application. where a significant merit is attributed to reaching the best trade-off between performance and weight. the compressor aerodynamic design problem can be stated as follows: For given pa. remarkable importance is attributed to maximize or minimize some compressor performance indexes or figures of merit. Finally. as some constraints could be turned into objectives. M Maximize (η. objectives which are intuitively conflicting each other. the problem can be set up in the following way: For given pa. technological and other constraints = g(X). For instance. Finally. it is worth analyzing how performance can be significantly affected by the choice in the design variables. Therefore. an intervention aimed at regulating the delivered power of the gas turbine has an effect also on the mass flow conveyed by the compressor. Structural. Ta. particularly cascade parameters. of course. Again. load-response) = f(X) Subject to: m =m(X) PR = PR(X) Matching Index (MI) = MI(X) Cost function = Cost function(X) Weight. minimizing compressor weight (at least from the aerodynamic point of view) implicates reducing the number of compressor stages and increasing individual stage loading. maximizing stall margin involves acquiring a proper insight of stall physics and minimizing stall losses. such problem can be tackled if proper stage geometry is foreseen. SM) = f(X) Minimize weight = weight(X) Subject to: m =m(X) PR = PR(X) Static thrust at sea level index = q(X) Matching Index (MI) = MI(X) Cost function = Cost function(X) Structural. maximizing adiabatic efficiency requires a deep understanding of the physics governing stage losses.4 Gas Turbines It is worth underlying that this might not be the general formulation. which have to be minimized either in design and off-design conditions. an aeroengine for military use. where a great importance is given both to the compressor peak efficiency and to the function called “load_response” which quantifies the rapidity of the compressor in adjusting the airflow delivered by means of IGVs and/or VSVs. driven by both experimental and numerical analyses. a much simpler approach can still be adopted which is based on pseudo-empirical relationships to explain and describe fluid dynamic losses and exit flow deviation. with the help of which significant results have been documented in the open literature.. in the following a brief summary of basic and advanced compressor aerodynamics is given. When NACA65 or Double Circular Arc (DCA) profiles are considered. 1999 for an exhaustive treatment of the subject.Advances in Aerodynamic Design of Gas Turbines Compressors 5 Based on the arguments above. 1996 confirms this. The reader is referred to Denton & Dawes. is by far the most used. with reference to a generic compression stage (Fig. seem to be among the most comprehensive and reliable for subsonic compressors. 4. Such an approach gives rise to the so-called “loss and deviation” correlation method. a flow deviation occurs at each cascade exit as a consequence of the non-infinite number of guiding blades. Today. 1960. among which the one proposed by Koch & Smith. for which the predictive models given by Miller et al. Mach number and three-dimensional effects taking place close to blade hub and tip. 1976. 1. Summary of compressor losses at design and off-design conditions Despite the remarkable advances regarding the physical origin of compressor losses. 1). 1961. Sketch of a compressor stage (left) and cascade geometries at midspan (right). A work by Schobeiri. camber and thickness. as well as because of the actual operating profile incidence. . flow deviation δ can be estimated using the following equation: δ= ( m )σ =1 ⎤ 1⎡ ⎛ dδ ⎞ ϑ ⎥ + Δδ ref + ⎜ ⎟ i − iref ⎢( Kδ )t (δ 0 )10 + K⎢ σb ⎝ di ⎠iref ⎥ ⎣ ⎦ ( ) (1) stator rotor Fig. A step further is required when inlet supersonic flows have to be dealt with (as in the case of transonic stages). together with those available in Lieblein. The fundamentals of CFD and its application to compressor design are beyond the scope of this chapter. a general theory for their estimation is not yet available. For the purpose here. As it is well known. perhaps the most reliable way to estimate losses accurately and generally is to use in fact Computational Fluid Dynamics (CFD). e.is w12 / 2 ζS = ⎡ h3 − h3t c2 2 / 2 (3) k −1 ⎫ k ⎪ ζ ≈ 1 / ⎡0. referred to the profile chord) which in turns depends on the Lieblein local diffusion factor: . Corrections are foreseen in order to modify the basic profile losses to account for Reynolds and Mach number effects. χ M is the Mach-based correction.5 ( k − 1 ) Mi2 ⎤ ⎨1 + 0.5 ( k − 1 ) Mi2 − ⎢( 1 − ϖ ) 1 + 0. Losses are computed for both rotors and stators using the following relation: ζR = ⎧ ⎪ h2 − h2 . one iref. A well established approach is to account for the various loss sources. according to the following equation ζ = ζ ( M = 0 ) χ R χ M +ζ sh + ζ s + ζ δ + K M i − iref ( ) 2 (2) where: ζ ( M = 0 ) is the basic loss coefficient for incompressible flow.5 ρ1 w1 ) o 2 ϖ S = ΔpS (0. ζ sh is the shock correction. secondary and tip-clearance ones. σ the cascade solidity. χ R is the Reynolds-based correction. ( Kδ )t = f (smax / l ) . 1976) but can be easily implemented numerically. ζ δ is the tip clearance loss coefficient. Moreover Δδ ref = f ( Mai . Addictive terms are finally introduced to estimate the shock wave losses when supersonic incoming flow occurs. x / b ) depends on the actual cascade Mach number and ( dδ / di )iref (i − iref ) takes into account the effect of off-design performance on deviation by estimating the actual incidence angle i with respect to the reference. the basic loss coefficient is a function of a series of parameters according to the following: ⎛ ϑ ⎞ σ ⎛ cos α i ⎞ ⎛ 2 H ⎞ ⎛ ⎛ϑ ⎞ σ ⎞ ϖ p = 2⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ 1 − H ⎜ l ⎟ cos α ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ l ⎠ cos α ex ⎝ cos α ex ⎠ ⎝ 3 H − 1 ⎠ ⎝ ⎝ ⎠ ex ⎠ 2 −3 (6) where ϑ / l is the non-dimensional momentum thickness of the blade boundary layer (i. Usually stage losses are divided into profile. function of the Mach number. o minimum loss. (δ 0 )10 is a basic deviation for symmetrical 10% thickness-to-chord profiles.6 Gas Turbines where K is a compressibility coefficient. in both on and offdesign operation. K M is the off-design coefficient. Terms in equation (1) are usually given in graphical form (Koch & Smith.5 ( k − 1 ) Mi2 ⎣ ⎦ ⎪ ⎩ ⎢ ⎣ Being ϖ the conventional total pressure loss coefficient: o 2 ϖ R = ΔpR (0. ζ s is the secondary loss coefficient.5 ρ 2 w2 ) ( ) k k −1 ⎤ +ϖ ⎥ ⎥ ⎦ ⎬ ⎪ ⎭ (4) (5) In estimating the profile losses. ( m )σ = 1 is a parameter referred to a sample cascade having solidity equal to 1 and ϑ is the profile camber. Reynolds correction is due to the fact that the shear stress boundary layer on the blade.61 ⎢ tan α 2 − σS ⎣ cm 2 ⎪ ⎪ ⎦⎭ ⎩ (7) while α i and α ex are the inlet and outlet flow angles of the generic cascade (i. in turn. which become nonnegligible when Mach number exceeds.5 c 2 S + c 3S . α i = β 1 and α ex = β 2 for a rotor cascade).5. to which losses are linked. whose values are found between 1.5 w1 R + w 2 R and c ∞S = 0. Secondary losses are caused both by friction on the endwalls and secondary vorticity located on planes perpendicular to the shaft axis. depends on the blade geometry and a work parameter referred to the blade midspan ( Ψ ).61 σR ⎪ ⎩ ⎡ c u ⎛ r2 ⎢ tan β 1 − m 2 tan β 2 − 1 ⎜ 1 − 22 ⎜ cm1 c m1 ⎝ r1 ⎢ ⎣ ⎞⎤ ⎫ ⎪ ⎟⎥ ⎟⎥ ⎬ ⎪ ⎠⎦ ⎭ c DRS = 2 c1 ⎧ ⎤⎫ cm 3 cos 2 α 2 ⎡ ⎪ ⎪ tan α 3 ⎥ ⎬ ⎨1.. respectively. depends on the chord-based Reynolds blade number according to the following: χR = ϖp ϖ p .15 ⎞ ⎛c ⎟ + Y ⎜ ∞S ⎟ ⎜w ⎠ ⎝ 1 3 3 ⎞ ⎟ ⎟ ⎠ 3⎤ ⎥ ⎥ ⎦ 3⎤ ⎡⎛ ⎞ (l / b) ⎢⎜ w∞R ⎟ ζ S _ vorticity = 0. 1960 secondary losses are linked to an energy dissipation coefficient cd which. to which the reader is referred for details. ( ) ( ) .3 and remarkable for M>0. A more rigorous modelling for secondary losses will break down the contribution due to the endwall friction and secondary vorticity according to the following (valid for a rotor blade): ζ S _ annulus ⎡⎛ ⎢⎜ w∞R = 0.e.004 χ R ( 1 + Y ) senβ1 ⎢⎜ w1 ⎣⎝ la / b 0.12 + . say. According to Suter. A special case occurs for supersonic cascades (incidence M>1). and H is a shape factor. 0.05 and 1. Shock correction applies only to supersonic blades and can be calculated reasonably well using the two-dimensional shock loss model provided by Miller et al.032 χ R Ψ a 1 + Y ) sen β 1 ⎢⎜ w1 ⎟ ( ⎠ ⎣⎝ ⎛c + Y ⎜ ∞S ⎜w ⎝ 1 ⎞ ⎟ ⎟ ⎠ (10) ⎥ ⎥ ⎦ where w∞R = 0. 1961.ref = cf c f ref (8) where c f = f (Re) is the shear stress coefficient of a smooth flat plate. Mach correction offers an explanation for compressibility effects. being the latter empirically determined: c d = χ R F Ψ + 0.004 ( ) (9) where F = f (la / b ) being la and b the blade axial chord and blade height.Advances in Aerodynamic Design of Gas Turbines Compressors 7 DRR = w1 w2 ⎧ cos 2 β 1 ⎪ ⎨1.75.2. for which χ M >1. while χ R is the Reynolds-based correction.12 + 0.ref = ζp ζ p . Kδ is an empirically derived coefficient. Another example is given by Wisler et al. whose calculation is based on the actual boundary layer displacement thicknesses at the root δ * R and at the tip δ *S of the blade: * δ R = δ * R0 + ψ ψ * δ '' δ S = δ *S 0 + δ' ψmax ψmax (12) being δ '' and δ ' the clearance gaps of the rotor and stator blades.8-1.8-2] when φ/φ* belongs to [0. 1989) has been predicted by the author and compared to available experimental data. A blockage factor can also be accounted for in order to estimate the correct mass flow delivered by a generic stage using the following expression. Traupel suggests the following expression for a rotor blade: ζ δ = Kδ ⎜ ⎜ ⎛ Δwt ⎞ 1 ⎟ u2 ⎟S senγ tS ⎝ ⎠ ⎛ w1s ⎜ ⎜ w ⎝ 1 ⎞ Dsδ ⎟ ⎟ D b ⎠ m 2 (11) where: γ tS is the blade stagger angle. .. where the map of the Rolls-Royce HP9 compressor stage (Ginder & Harris. the following blockage factor can be calculated: ξ =1−⎢ ⎢ ⎣ ⎡ rR +δ R rR ∫ ( ρw m − ρ wm 2π r dr − ) rS rS −δ S ∫ ( ρw ( m ⎤ 2 − ρ wm 2π r dr ⎥ / ρ wmπ rS − r 2 R ⎥ ⎦ ) ( ) (13) 2 where the actual mass flow rate is m = ξ ρ wmπ rS − r 2 . where a preliminary design study was conducted using correlations to identify an advanced core compressor for use in new highbypass-ratio turbofan engines to be introduced into commercial service in the 1980's. function of the ratio between actual and design flow coefficients. 1970. measured with respect to the tangential direction.: R ) ξ =1− * * 2 δ R rR + δ S rS 2 rS − r 2 R ( ) = 1 − 4 (D * R δR * + DS δ S ) 2 DS − D 2 R (14) Correlations presented above are able to give a reasonable insight into the loss mechanisms and to capture the correct entities for the various sources involved in both design and offdesign conditions. Advanced design techniques Independently from the particular case under study. An example of prediction obtained by the author using such an approach is given in Fig. and δ * R 0 and δ *S 0 the displacement thicknesses corresponding to null values of the gaps in the rotor and stator blades. respectively. δ is the tip clearance gap.3]. modern compressor design philosophy can be summarized as in Fig. proposed by Smith. 5. Consequently.e. 3.8 Gas Turbines Tip clearance losses are a complex function of blade geometry. ( Δwt / u2 )S is the work coefficient of the rotor. i. 2. 1977. its values are found in the range [0. tip gap and functional parameters. Within this process.5 10 10.5 8 8. Therefore. no effort is spent to account for flow variations other than those which characterize the main axial flow direction within each stage at a time. so that an iterative process occurs until a satisfactory preliminary design is obtained. Experimental and predicted map of the Rolls-Royce HP-9 compressor. .Advances in Aerodynamic Design of Gas Turbines Compressors 9 experimental Desi gn point Efficienc y predicted 6. technological and process constraints.5 9 9. where each stage characteristics are condensed into a single “design block”.5 Sur ge line (experimental ) Desi gn point Sur ge line (predicted) Com pressor ratio 4 5 6 7 8 9 10 11 Corrected mass flow [kg/s] Fig. A preliminary design is usually carried out at first. aiming at defining some basic features such as number of stages. 2. some early choices could be revisited and subject to aerodynamic criteria checking. stages are stacked together to determine the overall compressor design. inlet and outlet radii and length. Stage loading and reaction is established as well on the basis of preliminary criteria driven by basic theory and experiments. as well as restrictions on weight and cost. Such procedure is based on one-dimensional (1D) methods. to which basic thermo.and fluiddynamics equations are applied. In this framework. which will be described later on. regardless any mutual stage interaction.5 7 7. Then. play an important role that must be properly accounted for. Compressor design flow chart.1 Preliminary design techniques A simple meanline one-dimensional method usually forms the basis of a preliminary design. is the two-dimensional design (2D). Examples of such methods are almost uncountable in the literature (see. some design intervention is needed to account for the real three-dimensional. In this phase. the one developed by Casey. both direct and inverse design methodologies have been successfully applied. it is worth considering that the elementary compressor ratio. In the following. a synthesis of such methods is provided. To this respect. from which a characterization of both design and off-design multi-stage compressor performance can be carried out after some iterations. the compressor total pressure ratio is known from which the total number of compressor stages can be estimated. This is usually carried out using CFD models. e. if necessary optimized. the designer can use statistical indications based on typical values of admissible peripheral speeds and stage loading (see Fig. if necessary. among others. a blade to blade solver and/or a throughflow code. Numerical optimization strategies may be of great help in this case as the models involved are relatively simple to run on a computer. which include both cascade and throughflow models. especially tip clearance. where the running blade is modelled in its actual deformed shape. which can be easily derived from the Euler equation for an axial stage at the root-mean-square radius: . 5. More in details. the recent availability of powerful computers makes the analyses of multistage compressors an affordable task for most industries.g. Most advanced CFD computations include evaluation of complex unsteady effects due to successive full-span rotor-stator interaction. viscous flows in the stages. 3. For a given design condition. 1987). and an optimization algorithm which assists the designer to explore the search space with the aim of obtaining the desired objectives. that can be developed by a single stage obeys to the following equation. secondary flows and casing treatment for stall delay. 4). analyzed and.10 Gas Turbines Fig. Often an optimization involves coupling a prediction tool. π c . a fully three-dimensional (3D) design is carried out including all the details necessary to build the aerodynamic parts of the compressor. While traditional 3D analyses are aimed at evaluating and improving compressor performance of a single stage. Finally. distinct from the 1D procedure. In this case. A second preliminary step. the flow coefficient does not exceed 0. 4. it is well known that the work coefficient is today always less that 0. Moreover. R=287 J/(kgK). Preliminary estimation of the compressor number of stages based on typical peripheral mean velocities and stage loading. 5. u is the peripheral velocity at the mean radius. For instance. and cannot be chosen separately: 2 φ 2 = ⎜ z ⎟ = ⎨ M w 1 ⎢⎜ 1 ⎟ − ⎢⎜ u ⎟ 2 ⎝u⎠ ⎪ ⎣⎝ ⎠ ⎩ ⎛c ⎞ 2 ⎧ ⎪ ⎡⎛ a0 ⎞ 2 k−1 (1 − ε R − ψ / 2) 2 ⎫ ⎤ ⎪ 2 ⎥ − ⎡ε R + ψ / 2 ⎤ 2 ⎬ / ⎛ 1 + k − 1 M w 1 ⎞ ⎜ ⎟ ⎦ ⎥ ⎣ 2 ⎠ ⎪ ⎝ ⎦ ⎭ (2) Fig. finally. 1942 inlet flow angles never stay far away from 55 degrees. This is very useful for estimating the preliminary stage pressure ratio once the range for the other functional parameters has been settled. 6 displays this relation in graphical form for both industrial and aeronautical compressors. T10 the total temperature at stage inlet.6 and very rarely goes below 0. Actually. the work and flow coefficients are linked together via the blade degree of reaction ε R .Advances in Aerodynamic Design of Gas Turbines Compressors 11 Fig. M w 01 the Mach number of inlet relative velocity with respect the stagnation speed of sound. From the above equation.2 (at least for subsonic stages). due to theoretical arguments going back to Howell. η pol the estimated stage polytrophic efficiency. being the maximum theoretical stage efficiency in the .45 for an ordinary subsonic stage in order not to overload it and to limit stall susceptibility. ⎛ ⎞ k −1 ⎛ ψ ⎞ k −1 u2 2 = ⎜ 1 + ( k − 1 ) M w01 cos2 β 1 2 ⎟ π c = 0 = ⎜ 1 + ( k − 1) ψ⎟ ⎜ 0 ⎜ φ ⎟ p1 ⎝ kRT1 ⎟ ⎝ ⎠ ⎠ 0 p2 kη pol kη pol (1) where k is the ratio of specific heats for an ideal gas. a preliminary design chart can be obtained as reported in Fig. β 1 the mean inlet flow angle measured and. At the same time. ψ and ψ the work and flow coefficients. 7). the operating Mach number is less than 0. 5. neighbourhood of tan β m = 0. Preliminary compressor design chart.5 ( tan β 1 + tan β 2 ) =45° and the maximum flow turning in the order of 20° for a decelerating cascade.8 (see Fig. while transonic stages operate with 2 and more while maintaining an acceptable . Load and flow coefficients as functions of the relative Mach number for a given degree of reaction for aeronautical (left) and industrial (right) stages.5-1. 6.12 Gas Turbines Fig. This is the reason why modern subsonic stages can develop pressure ratios in the order of 1. Fig. Finally. but can go up to 2 and more at the tip of a transonic blade.75 for a subsonic cascade. 89 is by far one of the highest documented values for transonic bladings. 7.45 (front stages) and 0. Estimation of the number of compressor stages based on stage loading and mean circumpherential speed. the 1-D methods rely in the sequential calculation or assumption of the following quantities: peripheral mean stage rotor velocity (300-350 m/s for subsonic rotors. Fig.9. Fig. Based on these indications. the latter reaches values not very much higher than 0.Advances in Aerodynamic Design of Gas Turbines Compressors 13 value for the polytropic efficiency.6 (rear stages). 8. while 0. i.e. the total number stages can therefore be estimated from admissible stage compression (Figure 8). Without going very much into details. In a well designed subsonic stage. . Annulus radius ratio. Time evolution for compressor circumferential speed and stage loading. usually chosen between 0. Rhub/Rtip. up to 600 m/s for transonic ones). By imposing such a constraint. As a first check. Mean radius basic cascade characteristics (based in the Howell’s method or Mellor charts. 2D approach. 11). values between 0. 9. the values of stage area passage can be derived from the continuity equation (Fig. the axial Mach distribution along the stages must be calculated and a value not exceeding 0. from which the distribution of stage parameters along the mean radii can be obtained. 10. Stage stacking. To this purpose. 1957. a loop is required to satisfy all the design objectives and constraints. Choice of the stage degree of reaction (possibly around 0.92. 1956).14 Gas Turbines c2 α2 α1 β1 β2 u w2 1 w1 rotation c1= c3 2 u 3 Fig.66 can be assigned. technological and economic constraints. Because the stacking procedure is intrinsically iterative.5 is tolerated for both subsonic and transonic stages. while outlet stages often are given a higher value. Next. - .45 and 0. see Lieblein. see Emery et al. 1958. work and flow coefficients and subsequent determination of the velocity triangles (Fig. Result of stage stacking consists in the flowpath definition. Estimation of the number of compressor stages based on stage loading and mean circumpherential speed. Fig. Iteration. say from 0. Horlock. in order not to increase the exit Mach number (a condition which is detrimental for pneumatic combustor losses).. it is worth recalling that such value comes from a trade-off between aerodynamic. 9). For inlet stages.8 to 0. 1960): Calculation of the blade height at the stage exit based on acceptable blade aspect ratios. Estimation of the diffusion performance (based on acceptable Lieblein diffusion factors or De Haller numbers. the values of the hub-to-tip ratios must be defined. Mellor.5. 11. Lieblein’s Diffusion Factor (DLi) level versus solidity for given flow and work coefficient (left). In their work. Fig. a numerical methodology is used for optimizing a stator stagger setting in a multistage axial-flow compressor environment (seven-stage aircraft compressor) based on a stage-by-stage model to 'stack' the stages together with a dynamic surge prediction model. is presented. the flow angles and the degree of reaction of the compressor stage were obtained. assuming a fixed distribution of axial velocities. 1998. Numerical examples were provided to illustrate the effects of various parameters on the optimal performance of the compressor stage. 10. ψ diagram (right). 2005. A recent example of how 1D models can still be used in the preliminary design of axial compressors is given by Chen et al.Advances in Aerodynamic Design of Gas Turbines Compressors 15 Fig. while the objective function was penalized externally with an updated factor which helped to accelerate convergence.. A direct search method incorporating a sequential weight increasing factor technique (SWIFT) was then used to optimize stagger setting. the work coefficient. Iso De Haller number in the φ. Analytical relations between the isentropic efficiency and the flow coefficient. a model for the optimum design of a compressor stage. Corrected mass flow over stage area passage as function of the axial Mach number. Corrected mass flow /Passage 2 area [kg/(sm )] . In their work. Despite its relative simplicity. meanline 1D methods based on stage-stacking techniques still play an important role in the design of compressor stages as also demonstrated by Sun & Elder. The absolute inlet and exit angles of the rotor are taken as design variables. Remarkable developments in the design techniques have been obtained using such codes. . so that streamline conservation properties cannot be applied. the MTFM is numerically more stable than SCM. Domain sketch for throughflow calculations. They make use of cascade correlations for total pressure loss/flow deviation and are based on throughflow codes. Massardo et al. MTFM uses a fixed geometrical grid. despite stream function values must be interpolated throughout the grid. 12. 1968) and streamline throughflow methods STFM (Von Backström & Rows. matrix throughflow methods MTFM (Marsh. the compressor map in both design and off design operation can be obtained exhibiting high accuracy. while blockage factor that accounts for the reduced area due to blade thickness and distributed frictional force representing the entropy increase due to viscous stresses and heat conduction can be incorporated. As a result of the application of throughflow codes.2 Advanced throughflow design techniques (2D) Throughflow design allows configuring the meridional contours of the compressor. Three methods are basically used for this purpose: streamline curvature methods SCM (Novak. A distributed blade force is imposed to produce the desired flow turning. spanwise migration of airfoil boundary layer fluid and spanwise convection of fluid in blade wakes (Dunham. SCM has the advantage of simulating individual streamlines. The procedure allowed for optimization of the complete radial Fig.. 1999). On the other hand. 1967). However. Finally STFM is a hybrid approach which combines advantages of accuracy of SCM with stability of MTFM. These methods have recently been made more realistic by taking account of end-wall effects and spanwise mixing by four aerodynamic mechanisms: turbulent diffusion. turbulent convection by secondary flows. Other remarkable results consist in incorporating a throughflow code into a Navier-Stokes solver for shortening the calculation phase (Sturmayr & Hirsch. making it easier to be implemented because properties are conserved along each streamline but is typically slower compared to the other methods. 1990 described a technique for the design optimization of an axial-flow compressor stage. 1997). which are two-dimensional inviscid methods that solve for axisymmetric flow (radial equilibrium equations) in the axial-radial meridional plane (Fig. 12). Among others.16 Gas Turbines 5. as well as all other stage properties in a more accurate way compared to 1D methods. 1993). being the objective function obtained using a throughflow calculation (Fig. near the annulus walls. Optimization procedure proposed in Massardo et al. The diffusion factor was constrained to avoid designs involving flow separation. the solidity of a blade which maximized one objective (see. Direct methods These are design methods where a blade-to-blade geometry is first assessed and subsequently analyzed using available CFD flow solvers. A very interesting application of a throughflow multiobjective design optimization has been recently given by Oyama & Liou. a throughflow code based on the streamline curvature method is used along with a multiobjective evolutionary algorithm to design a four-stage compressor (Fig.3 Advanced cascade design techniques (2D) A great benefit in compressor design for maximum performance can derive from advanced 2D cascade aerodynamic design using both direct and indirect methods. 2002. Some examples were given of the possibility to use the procedure both for redesign and the complete design of axial-flow compressor stages.Advances in Aerodynamic Design of Gas Turbines Compressors 17 Fig. Then. Gradient-based optimization methods are still in use only for special “quadratic” cases. 14. and flow angles and solidities at the stator trailing edges were considered as design parameters. 1995) are preferable to other “local” methods since they have revealed to be powerful tools in handling multimodal. 14 (right). non convex and multi-objective problems. for example. 5. and low dynamic head. Among optimization techniques available today. The procedure made it also possible to obtain the full span distribution of design variables. In this paper. Total pressure and solidities at the rotor trailing edges.. In Fig.g. incorporated a viscous throughflow method into an axial compressor design system such that the meridional velocity defects in the endwall region and consequently blading could be designed that allowed for the increased incidence. left) for maximization of the overall isentropic efficiency and the total pressure ratio. . Howard & Gallimore. 1990 distribution of the geometry. 14). e. the final Pareto optimal solutions are plotted which reveal a significant superiority with respect to the baseline compressor from which the optimization started. Iterative methods perfectly suit for this purpose. Schwefel. 1993. evolutionary algorithms (Goldberg. 13). 1989. so that optimization loops are often used in the framework of this approach. 13. Fig. shape modifications take place and resulting geometries evaluated until an acceptable or even optimal configuration is found. using a gradient optimization method and an inviscid/viscous code.. On the other hand. 2000 and Küsters et al. 2002). From this point of view.18 Gas Turbines Fig. at least to predict flow quantities in the vicinity of the design point of the machine. 1997 faced the multi-objective optimization problem of maximizing the pressure rise and efficiency of compressor cascades with a Pareto-Genetic Algorithm and a NavierStokes solver.. Köller et al. 2000 developed a new family of compressor airfoils. 14. Since the large majority of the computational time is spent in the evaluation process of the objective function. a faster solution approach to calculate the flow field would be more appropriate. characterized by low total pressure losses and larger operating range with respect to standard Controlled Diffusion Airfoils (CDA). the use of Euler solvers with integral boundary layer approach are more desirable than Navier-Stokes codes. Until today. Throughflow optimization of a multistage compressor (from Oyama & Liou. the available evolutionary optimization techniques are not enough effective in exploiting information from a population of candidate solutions to the optimization . Obayashi. Pierret. the use of evolutionary techniques in combination with CFD codes for solving multi-objective optimization problems in compressor aerodynamics has been limited by the tremendous computational effort required. 1999 used an artificial neural network coupled with a Navier-Stokes solver to maximize the efficiency and/or operating range of two-dimensional compressor cascades and then staggered them in radial direction to obtain the three dimensional blade. 15). to maximize pressure ratio and minimize total pressure losses across the cascade for a given inlet Mach number. . e. From Benini & Toffolo. A number of different design choices can be carried out to reach this scope.g.yCL(i)) (x(i).g. so that the number of generations required to get the optimum is usually great. the shape of the profile plays an important role because it affects the nature of the boundary layer on the suction side and therefore the amount of profile losses. one can impose a constraint regarding maximum allowable total pressure losses over the operating range of the cascade.. Moreover. In fact.Advances in Aerodynamic Design of Gas Turbines Compressors 19 problem. the flow may be turned by a high cambered profile at low incidence angles or. or may adopt a low solidity cascade to minimize the friction losses for a prescribed pressure rise.yCL(i)+δ (i)) (x(i). An option to handle this problem is to parameterize the shape of the airfoil first.. On the other hand.yCL(i)-δ (i)) θ inl ---■ θ out Bezier Pol ygon Bezier Control Fig.. the designer may use a high solidity cascade in order to decrease the aerodynamic loading on a single profile. the following condition had to be verified at each operating point i. inlet and outlet flow inclinations (fixed flow deflexion).5 deg. 2002. In this respect. for a generic cascade. I-type grid used in the simulations of a compressor cascades (right). by a low cambered profile having marked positive incidence. by using Bézier parametric curves (see Fig. ±2. squares represent control points of Bezier curves (left). All these choices involve a decision-making process that makes the design a challenging task. Considering a cascade of airfoils. i. the ultimate goal of compressor cascade design is to create a blade with maximum pressure rise and minimum total pressure loss along with an acceptable tolerance to incidence angles variations. (x(i). A powerful evolutionary optimization code was developed by Toffolo & Benini. being ω the total pressure loss coefficient of the cascade. a proper problem formulation is needed. 2004). ωi / ω * ≤ 2 ∀i = 1. 5 . thus penalizing the convergence process. e. for instance the total pressure loss can be measured in five operating conditions defined by βi-β1*=0. thus reaching the maximum pressure rise with the whole blade row.. 2003 to support the development of a new design methodology of optimal airfoils for axial compressors (Benini & Toffolo.e. ±5 deg and compared to the one of the design: to satisfy the constraint. equivalently. Geometry parameterization of an airfoil using Bezier curves. 15. in order to assure efficient off-design operation and acceptable profile thickness. Next. NACA 65-12-10 and NACA 65-15-10 are dominated by individuals A. 16 right). In particular. a sudden drop in the profile efficiency is unavoidable. Fig. A typical multiobjective evolutionary strategy (Schwefel. 16. 1995) with genetic diversity preserving mechanism (GeDEM) can be used (Fig. Initial random population Parents’ selection Reproduction (crossover + mutation) Evaluation (Pareto ranking) A B C A1 B1 C1 GeDEM No STOP Yes Max generation no. PR=Pressure ratio. the cascade of NACA 65-8-10. the required cascade performance is specified and the blade shape is sought accordingly.? Survival of the fittest Fig. as the flow turning moves toward its maximum. left) to obtain Pareto-optimal solutions (Fig. Comparison between non optimal (left) and optimal (right) Mach number contour plot in a transonic compressor cascade (from Ahmadi. w=total pressure loss coefficient. Although widely used in both academia and industry. and by individuals A1. The shape of the Pareto front confirms that at low pressure ratios it is possible to increase profile loading without penalizing efficiency in a very significant way. C with respect to profile efficiency (PR being fixed). on the other hand. B1. Scheme of the optimization used for cascade optimization (left).20 Gas Turbines An efficient algorithm can be used to handle the problem. From Benini & Toffolo. 1998). C1 with respect to pressure ratio (profile efficiency being fixed). 16. Inverse methods In inverse design. It is worth noting that the individuals belonging to the Pareto front “dominate” the cascades of NACA 65 profiles. they are far from . Pareto front of the optimization compared with performance figures of NACA 65 cascades (right). 2002. B. 17. is already available.Advances in Aerodynamic Design of Gas Turbines Compressors 21 being as accurate as direct methods. Examples of 3D designs of both subsonic and transonic compressor bladings are today numerous in the open literature. or mechanical constraints) should not be part of the fitness function. obtained using a combination of 1D and/or 2D methods. The object of present optimization was to maximize efficiency. Finally. For numerical optimization. 1987. Moreover. 17). 5. 1945. velocity or Mach number distribution (Lighthill. 2000 developed a numerical optimization technique combined with a three-dimensional Navier-Stokes solver to find an optimum shape of a stator blade in an axial compressor through calculations of single stage rotor-stator flow. Direct methods involving optimization techniques and direct objective evaluation Among others. Particular effort has been devoted to the design of the fitness function for this application which includes non-dimensional terms related to the required performance at design and off-design operating points. Leonard & Van Den Braembussche. Sieverding et al. when a good starting solution. a powerful blade-to-blade flow solver and an optimization technique (breeder genetic algorithm) with an appropriate fitness function. it has been found worthwhile to examine the effect of the weighting factors of the fitness function to identify how these affect the performance of the sections. performance is defined by the design specification of either the flow properties on one or both sides of the blade. particularly that inviscid flow equations (Euler equations) are solved. and the golden section method was used to determine optimum moving distance along the searching direction. who implemented a cell-vertex finite volume method on unstructured triangular meshes. The method was first validated for a compressor cascade and then used to redesign a transonic ONERA cascade with the aim of removing the passage shock (Fig. 2004 showed an example of advanced 3D design of industrial compressors blades. The design method then provided the blade shape that would accomplish this loading by imposing the appropriate pressure jump across the blades and satisfying the blade boundary condition. searching direction was found by the steepest decent and conjugate direction methods. The method combined a parametric geometry definition method. 1998. In this design method. The reason for this relies in the simplifications which characterize them. typically pressure. These are usually very expensive procedures in terms of computational cost such that they can be profitably used in the final stages of the design. It has been found that essential aspects of the design (such as the required flow turning. large computational resources are necessary to obtain results within reasonable industrial times. 1992). the mass-averaged swirl schedule and the blade thickness distribution were prescribed.. but need to be treated as so-called "killer" criteria in the genetic algorithm. A noticeable application of inverse methods for the design of transonic compressor cascade is given by Ahmadi. Giles & Drela. In 2D cascades. Lee & Kim. It is worth .4 Advanced 3D design techniques Direct methods Advanced optimization techniques can be of great help in the design of 3D compressor blades when direct methods are used. An optimum stacking line was also found to design a custom-tailored 3-D blade for maximum efficiency with the other parameters fixed. which typically require a wider range from surge to choke than typical gas turbine compressors in order to meet the high volume flow range requirements of the plant in which they operate. Computational time was huge. Fig. blade geometry was parameterized using three profiles along the span (hub. A multiobjective design optimization method for 3D compressor rotor blades was developed by Benini. where the optimization problem was to maximize the isentropic efficiency of the rotor and to maximize its pressure ratio at the design point. Direct objective function calculation was performed iteratively using the three-dimensional Navier-Stokes equations and a multi-objective evolutionary algorithm featuring a special genetic diversity preserving method was used for handling the optimization problem. the effect of blade lean was achieved. each of which was described by camber and thickness distributions.files’ control point with respect to the hub profile. Performance map and Mach number contours of baseline and optimized compressor configurations (from Benini. 18). . both defined using Bézier polynomials. The blade surface was then obtained by interpolating profile coordinates in the span direction using spline curves. Performance enhancement derived from a drastic modification in the shock structure within the blade channel which led to less severe shock losses (Fig. midspan and tip profiles). 2004). 18. 2004. In this work. using a constraint on the mass flow rate.22 Gas Turbines noting that the system has been tested on the design of a repeating stage for the middle stages of an industrial axial compressor and the resulting profiles showed an increased operating range compared to an earlier design using NACA65 profiles. By specifying a proper value of the tangential coordinate of the first midspan and the tip pro. involving about 2000 CPU hours on a 4-processor machine. Results confirmed the superiority of optimized leaned profiles with respect to the baseline configuration as far as efficiency and pressure ratio were concerned. are chosen such that they satisfy the functional. that is. which eliminates the dependency of the optimality condition on flow variables. called adjoint variables. but the optimum for adiabatic efficiency is located far from them. and radial basis neural networks. remarkable. 1996. or adjoint equation. Samad et al. as in 3D designs of complex geometry. employing as few data points as possible for constructing a surrogate model. the use of approximations of the objective functions is becoming a popular technique. an inverse method was presented which is based on . at a negligible computational cost. as well as the total pressure and total temperature ratios. This is often referred to as a “response surface methodology” (RSM) and the practice of building an approximation of the true objective function is named “metamodelling” or “surrogate model construction”. lean. 2004). However. Inverse methods In the last two decades. The optimized compressor blades yielded lower losses by moving the separation line toward the downstream direction. Quite a new approach to the 3D design of axial compressor bladings has been recently proposed by Tiow. 2008 multiple surrogate models for compressor optimization were considered including polynomial response surface approximation. 2002. Demeulenaere & Van Den Braembussche. It was found that using multiple surrogates can improve the robustness of the optimization at a minimal computational cost. three-dimensional inverse design methods have emerged and been applied successfully for a wide range of designs. Direct methods involving optimization techniques and adjoint equations Another. Three design variables characterizing the blade regarding sweep. where the goal is to minimize a nonlinear objective function subject to the governing flow equations as constraints. Adjoint methods are characterized by the definition of a classical Lagrangian functional. Once that the response surface was constructed. direct design optimization procedure makes use of adjoint methods (Chung. In this work. 1991. that is. The optima for total pressure and total temperature ratios were similar.. and fidelity. the adjoint formulation enables the gradients of an objective function with respect to all design variables to be obtained simultaneously. The formulation tries to encompass the drawbacks related to the long time required by traditional optimization techniques to converge.Advances in Aerodynamic Design of Gas Turbines Compressors 23 Direct methods involving optimization techniques and surrogate methods In order to accelerate convergence toward the design optima without using intensive calls of a CFD solver. 1999). the assessment of the performance of surrogate models is of critical importance. In a recent work. Dulikravich & Baker. an adjoint sensitivity code needs to be built corresponding to the flow solver. a sequential quadratic programming was used to search the optimal point based on these alternative surrogates. offering high accuracy in representing the characteristics of the design space. Kriging. The optimization was guided by three objectives aimed at maximizing the adiabatic efficiency. Considering the competing requirements of computational economy. For the computation of adjoint variables. obtaining accurate adjoint sensitivities is inherently difficult in internal flow problems due to the close proximities of the boundaries. The Lagrangian multipliers. and skew were selected along with the three-level full factorial approach for design of experiment. However. involving both radial/mixed flow turbomachinery blades and wings (Zangeneh. This implies that a shape optimization based on the adjoint formulation becomes economical when the design involves a large number of design variables. 20. Moreover. 2002 joins the capabilities of an inverse design with the search potential of an optimization tool. The entire computation required minimal human intervention except during initial set-up where constraints based on existing knowledge may be imposed to restrict the search for the optimal performance to a specified domain of interest. in this case the simulated annealing algorithm (Kirkpatrick et al. Two generic transonic designs have been presented. 19. Fig. contrary to the methods cited above. 1987. Fig. where loss reductions in the region of 20 per cent have been achieved by imposing a proper target surface Mach number which resulted in a modified blade shape (Fig.. the methodology proposed by Tiow. 1983).24 Gas Turbines the flow governed by the Euler equations of motion and improved with viscous effects modelled using a body force model as given by Denton. However. the methodology is capable of providing designs directly for a specific work rotor blading using the mass-averaged swirl velocity distribution. 19). a new design (prescribed by inverse mode). one of which referred to compressor rotor. Comparison of blade loading distributions of an original supersonic blade. and a reference blade (R2-56 blade) for a given pressure ratio (left). . 2002). 2003). comparison of passage Mach number distributions at 95% span (from Dang et al. Surface Mach number and geometry of inverse designed and final blades (from Tiow. Nevertheless. either stationary or aeronautical. To enhance the potentialities of such methods. thus leading to a more accurate definition of the flow path of both meridional and cascade geometry.Advances in Aerodynamic Design of Gas Turbines Compressors 25 An interesting application of a three-dimensional viscous inverse method was developed by Dang et al. such as direct or indirect methods driven by advanced optimization algorithms and CFD. . Detailed 3D aerodynamic design remains peculiar of single stage analyses. In view of the above. 3D design optimization techniques can realistically be used if local refinements of a relatively good starting geometry is searched for. simplified design methods are mandatory. more often assisted by solid mathematical tools that help the designer to complete his/her skills and experience. transonic bladings make it possible to reduce the number of stages for a prescribed total compression ratio. the availability of advanced materials for blade construction makes it possible to rich levels of aerodynamic loading never experienced in the past while preserving high levels of on-off design efficiency. 2D methods supported by either throughflow or blade-to-blade codes in both a direct and an indirect approach. where the number of design iteration can be potentially reduced by an order of magnitude if local derivatives of physical quantities with respect to the decision variables are carefully computed. Results in Fig. Advanced techniques can be used in all stages of the design. optimization algorithms can be quite easily used to drive the search toward optimal compressor configurations with a reasonable computational effort. Plenty of design optimization techniques has been and are being developed including standard trialand-error 1D procedures up to the most sophisticated methods. thus leading to huge savings in compressor costs. 2003 ad applied to the design and analysis of a supersonic rotor. 20 showed that an optimum combination of pressure-loading tailoring with surface aspiration can lead to a minimization of the amount of sucked flow required for a net performance improvement at design and off-design operations. the latter is an approach suitable for verification and analysis purposes. 6. On the other hand. Other very promising techniques include adjoint methods. or meanline methods. where surrogate models of the objective functions are constructed. if more general results are expected. In fact. continuous effort is currently being spent in building advanced design techniques able to tackle the problem efficiently. thus with a limited design applicability. To properly design such machines. can be used afterwards. However. such as those based on supervised learning procedures. cost-effectively and accurately. although several works have described computations of multistage configurations. correlation-based prediction tools for loss and deviation estimation can be calibrated and profitably used for the preliminary design of multistage compressors. In the field of 1D. weight and complexity. This holds especially for highly-subsonic and transonic blades. either in steady and unsteady operations. the passage shock was weakened in the tip region where the relative Mach number is high. Conclusion Gas turbine compressors. However. thus leading to stage pressure ratios of 2 and more. multiobjective and multicriteria problems are to be dealt with which claim for rigorous and robust procedures. where tangential velocities are now becoming higher that 600 m/s. have reached a relatively mature level of development and performance.. where aspiration was applied to enhance the operating range of a compressor. By prescribing a desired loading distribution over the blade the placement of the passage shock in the new design was about the same as the original blade. ASME paper 86-GT-144. L. L. 1199-1205. Issue 2. Modelling of spanwise mixing in compressor through-flow computations. The present Basis of Axial Flow Compressor Design: Part 1 Cascade Theory and performance. NACA Rept. D. M. No. M. (2004). Dulikravich. No. Journal of Turbomachinery. Erwin J. Vol. AGARD Pep Working Group 18: Compressor Test Case E/CO-3. & Drela. AlAA Paper 2004-0027. C. K. C. ISSN: 0001-1452. 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No. Threedimensional inverse method for turbomachinery blading design. & Gallimore. Wu. (1986). Martin G. Applied Energy. . References Ahmadi. ISSN: 0957-6509. & Larosiliere. Luo. No. (2005). Part C. M. (1957). 4. Emery J. pp. (1993).V. Viscous Throughflow Modeling for Multistage Compressor Design. Herrig L.. (1998). T. Sun. 1368. J. Vol. (1989).. C2. Benini. 18. Systematic Two-Dimensional Cascade Test of NACA 65-Series Compressor Blades at Low Speeds. 296-305. M. Howell. Development of High-Performance Airfoils for Axial Flow Compressors Using Evolutionary Computation. Vol. Demeulenaere. Vol. F. R. Two-dimensional transonic aerodynamic design method. J. 544-554. Optimized efficiency axial-flow compressor. 3. D. Vol. A. pp. Aerodynamic Design of 3D Compressor Blade Using an Adjoint Method. (1958). (1989). M. (1996).. (2003). J. Journal of Mechanical Engineering Science. Denton J. (1942). pp.26 Gas Turbines 7. UK.. Ginder. MA. Design of Aspirated Compressor Blades Using Three-Dimensional Inverse Method. J. NASA/TM—2003-212212. Dang. S. Goldberg. pp. & Toffolo. J. ASME paper 96-GT-39.. Reading. pp. G. P. D.B.. Aeronautical Research Council Reports and Memoranda. Axial-flow Compressors. Turbomachinary Efficiency Prediction and Improvement. D. The use of a distributed body force to simulate viscous effects in 3D flow calculations. Giles. A mean-line prediction method for estimation the performance characteristics of an axial compressor stage. 211. & Lee. 559-565. (1999). M. Journal of Propulsion and Power. 9. 213. No. E. 81. N. Denton. 115. Chen. E. (1987). Vol. Van Rooij. R. 20. Vol. A. ISBN: 0852986300. ISSN: 0306-2619. IMechE Proc. A. 2095. ISSN: 0748-4658. Three-Dimensional Multi-Objective Design Optimization of a Transonic Compressor Rotor. 107-124. Q. (1987). . Pierret. Shock Losses in Transonic Compressor Blade Rows. No. H. (2000) Design optimization of axial flow compressor blades with three-dimensional Navier-Stokes solver. Cambridge. Jr (1961). Journal of Turbomachinery. S. Surrogate Modeling for Axial Compressor Blade Shape Optimization. ISSN: 0889504X.-Y. Lieblein. 478-490. W. Vol. (1999). Vol.. (1945).-Y. 3509. 220. MIT. Koch. ISSN: 0889-504X. Journal of Turbomachinery. ASME).. Incidence and deviation angle correlations for compressor cascades. ISSN: 0748-4658. Journal for Engineering and Power. S. pp. Quagliarella et al. pp. 112. pp.T. Development of Advanced Compressor Airfoils for Heavy-Duty Gas Turbines – Part II: Experimental and Theoretical Analysis. G. S. 98. M. Marsh. & Vecchi. Axial Flow Compressor Design Optimization: Part II—Throughflow Analysis. (1997). 553-560. VKI Lecture Series 1999-02 on Turbomachinery Blade Design Systems. Kim. M.. No. In: Genetic Algorithms in Engineering and Computer Science. & Schreiber. (1960). The NACA 65-Series Cascade Data. A. R. 671–680. Vol. KSME International Journal. New York. Vol. & Shyy. R. & Mönig. 406-415. Köller. Aeronautical Research Council. A digital computer program for the throughflow fluid mechanics in an arbitrary turbomachine using a Matrix Method. Lee S.. (2000). 9.-A. Haftka. Streamline curvature computing procedures for fluid-How problems. Mönig. No. Science. No. (1976). R. 3. 405411. A new method of two-dimensional aerodynamic design. & Hartmann M. 4. Obayashi. pp. C. 302-310. ISSN: 0889-504X. B. pp. 2. H.. & Liou. T.R. pp. A. L. Trans. Vol.. 24. 3. . D. 83. ASME Journal of Engineering for Power. Three-Dimensional Blade Design by Means of an Artificial Neural Network and Navier-Stokes Solver. MA..3. (1983). (1956). Lewis. Journal of Turbomachinery. E. Schreiber. M. 397-405. Vol. Vol. 89. pp. Lighthill. 122. pp. Multiple (2008)..-Y. Mellor G. Satta. Journal of Turbomachinery. K. U. 575–587. 114. K. H. Küsters. Oyama. Aeronautical research Council RxM 2104.. P. Gelatt. & Smith. Development of Advanced Compressor Airfoils for Heavy-Duty Gas Turbines – Part I: Design and Optimization. Eds. & Van Den Braembussche.. U. Two-dimensional Transonic aerodynamic design method. No. Novak. R. R. Leonard O. & Kim. Küsters. pp. Vol. Power (Trans. Multiobjective Optimization of a Multi-stage Compressor Using Evolutionary Algorithm.Advances in Aerodynamic Design of Gas Turbines Compressors 27 Kirkpatrick. C. B.J. ISSN: 1226-4865. A. A. AIAA paper 2002-3535. Miller. 122. Gas Turbine Laboratory Charts. pp. 82. (1992). Köller. No. Massardo.-S. C. 411-424. Trans. S. (2002). Optimization by simulated annealing. Eng. Vol. J. July. & Marini M.. Pareto Genetic Algorithm for Aerodynamic Design Using the NavierStokes Equations. (1967). ASME Transactions. (1968). Loss sources and magnitudes in axial-flow compressors. Samad. G. H. ASME Journal of Basic Engineering. Journal of Propulsion and Power.W. (2000). Wiley. Vol. ISSN: 0889504X. 235– 242.-A. 1005-1012. 14. Goel.. Vol. (1990). pp. Yiu. 5. Casing Boundary Layers in Multistage Axial Flow Compressors.. n. ISBN: 0471571482. No. NASA Report -CR-135133. (1995). & Casey. 1. Tokyo. Numerical optimization of a stator vane setting in multistage axial-flow compressors. Proceedings of the Institution of Mechanical Engineers. pp. Throughflow model for design and analysis integrated in a three-dimensional Navier-Stokes solver. Wiley. No 4. L. Volume 11. (1993). ETH Zürich. ISSN: 0271-2091. 59-73. pp. (2003). The streamline through-flow method for axial turbomachinery flow analysis. Suter. & Zangeneh M. Evolution and optimum seeking. Journal of Turbomachinery . Vol. M. Schwefel. (1960). 4. Part A: Journal of Power and Energy. Part A: Journal of Power and Energy. W. T. T. R.W. 2.. A. pp. pp. Zangeneh. C. J. ISSN: 0957-6509. P. Genetic Diversity as an Objective in Evolutionary Algorithms. pp. W. & Benini. 347 . & Smith. 212. Part A: Journal of Power and Energy. 599–624. Casing Boundary Layers in Multistage Axial Flow Compressors. 3. ISSN (printed): 1023-621X. Wisler. C. Jr. . Preliminary design study of advanced multistage axial flow core compressors. 151-167. ISSN: 0889-504X. H.H. ISSN: 0957-6509. H.-P. Volume 126. Evolutionary Computation. B. Japan. Elsevier. Vol. L. No. No. L. 163-177. A. ISSN: 0957-6509. (1970).28 Gas Turbines Schobeiri. Dzung Ed. & Elder. Mitt. 2. C. (1996). Elsevier. International Journal of Rotating Machinery. M. International Journal of Numerical Methods in Fluids. Tiow. Flow Research in Blading.H. Design of Industrial Axial Compressor Blade Sections for Optimal Range and Performance. pp. 13. Proceedings of the Institution of Mechanical Engineers. (2002). Toffolo. 247-259. in L. L. Turbomasch. D. T. Ribi. H. pp. 3. Smith. C. ISSN 10636560. Theoretische Untersuchung uber die Seitenwandgrenzschikter in Axialverdichtern. 213. (1999). pp. No. Therm. (1977).).354. E. Koch. Inst. in Flow Research in Blading (L. (1970). Smith. F. Application of simulated annealing to inverse design of transonic turbomachinery cascades. (1998). 323-332. Von Backström & T. Dzung. & Hirsch. Vol. Papers from the Eleventh International Symposium on Air Breathing Engines. (1991). A compressible three-dimensional design method for radial and mixed flow turbomachinery blades. 263-273. Ch. (2004). Part I: Theoretical Aspects. W. Proceedings of the Institution of Mechanical Engineers. Vol. Vol. Sieverding. K. & Roos. Sun. F. No. Advanced Compressor Loss Correlations. Sturmayr. 216.. M. New York. USA. and Households were 34%. Baltimore. PhD (Illinois). electric power. 12-13 October 2004]. Transport.2%). Baltimore. and industry were 20%. In a 2095 scenario limiting the GHG to 550 ppm CO2. 12-13 October 2004]. 12-13 October 2004 In the EU. Introduction Global CO2 emissions by sector in 1990 for transportation. Baltimore. in both developing and developed countries. USA.2 Exergy and Environmental Considerations in Gas Turbine Technology and Applications BSME. GDP by region in the figure below for the period 1950-1997 shows [IPIECA Workshop. 21%. 0% and 38% respectively [IPIECA Workshop. synfuels & hydrogen production. 1% and 17% respectively [IPIECA Workshop. The Transportation sector breakdown was Road (71. Baltimore. while more cost-effective emission reductions are found in the electric power and the industry sectors [IPIECA Workshop. as the worldwide passenger travel vs. It is argued that the high cost of alternatives. and 11%. 12-13 October 2004]. buildings. buildings. and industry are 40%. Sea . USA. sectoral CO2 emissions in 2005 for Energy. 19%. 27%. MSME(Iowa State). 23%. synfuels & hydrogen production. 15%. 27%. USA. 12-13 October 2004]. While it is noted that climate change scenarios are replete with assumptions. and the strong demand for mobility. USA 1. Richard ‘Layi Fagbenle IPIECA Workshop. the sectoral CO2 emissions for transportation. the global growth of the transportation sector is undeniable. USA. electric power. limits the effects of climate policies on the transportation sector. Baltimore. Industry. 2008. From: Rail Transport and Environment.30 Gas Turbines From: Rail Transport and Environment. page 5 – Facts & Figures. page 20 – Facts & Figures. Nov. Nov. 2008 . 5%). Nov. from which the Transportation sector had the second largest share of 31% after the Households & Services sector. Aviation (11.Exergy and Environmental Considerations in Gas Turbine Technology and Applications 31 and Inland Waterways (14. page 5 – Facts & Figures. From: Rail Transport and Environment. 2008 [Rail Transport and Environment. A similar trend would be found in other regions of the developed world which accounts for the bulk of the global energy consumption and carbon emission.9%). page 19 – Facts & Figures. Nov. Energy efficiency is of utmost importance in addressing the climate problem. 2008]. Similarly. Transportation of 100 tons of cargo for a distance of 700 km between the Netherlands and Switzerland generates the local pollution information as shown in the figure below: From: Rail Transport and Environment. . Aviation’s share of the Transportation sector energy consumption was 14%. second to Road Transport. Some significant strides have been made by some sub-sectors as the figure below indicates. local air pollution data for NOx and PM10 appears below for a journey of 545 km by three modes of transportation. Nov. 2008. page 5 – Facts & Figures. The sectoral energy consumption for 2005 appears in the figure shown below. From: Rail Transport and Environment. page 22 – Facts & Figures. . page 11 – Facts & Figures. 2008. 2008. Nov.32 Gas Turbines From: Rail Transport and Environment. a look at the noise profile of some modes of transportation is instructive. Nov. Finally. the Airline Industry Information publication of 16 January 2009 reported that the US Federal Aviation Administration (FAA) has announced the results of a commercial airline test flight using a mixture of jet fuel and biofuel derived from algae and jatropha plants early in January 2009.: non-isentropic compression from the atmospheric inlet conditions of the compressor to the isobaric (constant-pressure) combustion of the fuel in the combustion chamber. 2. sectors which have been shown to be responsible for most of the carbon emissions globally. However. We shall consider some of these issues in this chapter. The Brayton open-cycle components – simple cycle and combined cycle gas turbines Combustion Chamber/Combustor Compressed air from the compressor (either centrifugal or axial-flow type) flows directly into the combustion chamber (such as that shown in Fig. 2008].Exergy and Environmental Considerations in Gas Turbine Technology and Applications 33 From the above. Gas turbines are employed in the air transportation sub-sector as well as in industry generally. It is claimed that air transport accounts for some 2-3 per cent of all anthropogenic CO2 emissions [IPIECA Workshop. derived from a 50/50 blend of synthetic Fischer-Tropsch fuels and petroleum-derived fuels. viz. USA. 2. being taken through a series of processes. all of which is done in a continuous flow process. all of which is to be carried out with minimum pressure loss. As of 2004 IPIECA Workshop. 2. Industrial.2 and Fig. 2010] as well as second generation biofuels from 50:50 blend of jathropha oil and standard A1 jet fuel [The Seattle Times. and then followed by adiabatic (non-isentropic) expansion of the hot gases and finally discharging the gases into the atmosphere. Hence it is imperative to sustain the current drive for improvement in the energy.3 shows a typical turbine stage blades. several test flights have been undertaken with synthetic jet fuel derived from natural gas [Airline Industry Information. The energy transfer between the fluid and the rotor in the compression and expansion processes is achieved by means of kinetic action rather than by positive displacement as occurs as in reciprocating machines. Baltimore. These processes follow the Brayton cycle processes. Substantial volumes of air and combustion gases are moved smoothly and vibration-free through the gas turbine at very high velocities in an axial flow machine. exergy and environmental performance of gas turbines in general (land. The Turbine Chamber of a 3-stage gas turbine plant is shown in Fig. In June 2009. it is clear that just as the other sectors are called upon to reduce their GHG emission. the aviation fuels subcommittee of the ASTM International was reported to have approved specifications for synthetic aviation fuel. 2. the same should hold for the transportation sector. there was no substitute envisioned for jet fuel neither was there any niche alternative fuel on the horizon. 31. Dec. between 2008 and 2010. 12-13 October 2004]. May 3. and the Transportation Sectors. Similarly. and marine gas turbine technology).1 below) in a Brayton open simple cycle gas turbine where part of it ( < 1/3) is used in a direct-fired air heater to burn the fuel after which the remaining air is mixed with the combustion products. Gas turbines are employed in the Energy. aviation. . Minimization of pressure is critical at all stages from inlet to the compressor to entry into the turbine to ensure optimal power production from the gas turbine. D.1... D. The Turbine Chamber of a 3-stage turbine plant. [From Shepherd. Introduction to the Gas Turbine. 2.2. D. . Inc. 2.G. Fig.G. D. [From Shepherd. Van Nostrand Co. Van Nostrand Co..34 Gas Turbines Fig. A Combustion Chamber Can. Inc. Introduction to the Gas Turbine.. 0 13. New gas turbine fuels.01 0. D.3 Hydrogen 14.8 9. Table 4-1 gives the ultimate analysis of some liquid fuels.Exergy and Environmental Considerations in Gas Turbine Technology and Applications 35 Fig.6 12.1 85. Gas turbine fuels – conventional and new fuels Conventional gas turbine fuels currently in use are exclusively liquid and gaseous and usually hydrocarbons. 1970).3 0.4 8. 6 fuel oil).5 Sulfur 0. Conventional gas turbine fuels – Liquid and gaseous fuels Conventional gas turbine liquid fuels include the range of refined petroleum oils from highly refined gasoline through kerosene and light diesel oil to a heavy residual oil (Bunker C or No.9 1. Fuel 100 Octane petrol Motor petrol Benzole Kerosene (paraffin) Diesel oil Light fuel oil Heavy fuel oil Residual fuel oil Carbon 85.. .5 91. Inc. [From Shepherd. 1. Van Nostrand Co.1 1.0 Table 4. Units by Eastop & McConkey.4 2.G.1..4 11.2 Ash.3 86.7 86.3.1 0.I.8 12. Typical turbine stage.1 0. D. S.1 88.3 86. include the synthetic Fischer-Tropsch aviation jet fuels and the second generation biofuels. 2nd ed. (From Applied Thermodynamics for Engineering Technologists.9 14. Ultimate analysis of some liquid fuels.2 86. 4. etc. Introduction to the Gas Turbine.. 3. Table 4-2 below also indicates some of the key properties of some of the many known hydrocarbons. Solid gas turbine fuel technology is still in the research and developmental stages. as mentioned earlier in the Introduction. Units conversion done by Prof. Tetraethyl lead Table 4. Aromatics CnH2n-6 Xylene 21.8 -30 -10 18.61 0.519 40. Performance No.05 388.194 10.65 921.4 22.80 ……… 2256. Air.7 182. 10. oC -161.1 -88.1 3606.9 81.1 82 Specific Gravity HHV kJ/kg LHV kJ/kg Mixture kJ/m3 Octane Rating CH4 C2H6 C3H8 C4H10 C5H12 C7H16 C7H16 C8H18 C10H22 C12H26 C16H34 C18H38 C3H6 C4H8 C6H12 C5H10 C6H12 6.1 56.7 3353. ……… ……….749 0.6 -25 -107.1 3576.6 Formu . Gas CnH2n+2 3. Aromatics CnH2n-6 Toluene 20.5 49.774 0.240 42.5 103.3 27. Water 26. LPG CnH2n+2n Propane 4. S.691 3241. -60 ……… …… 100 …… 43-149 -191. 2.0 58.799 47.043 45.49 307.4 3610.1 78. …….86 337.9 216.2 77. Olefins CnH2n Propene Butene-1 14.3 49..0 …….22 ……… ……… ……… 77 110a 104a 105a 98 99 …… …… …… …… 140a …… 84 68 95 …… <75 <75 …… …… …… …… 78 …… 0.613 44.1 92.8 -117..86 29.690 0.106 26. Wt. Richard Fagbenle. SIT – Self-ignition temperature. kJ/kg 576. Alcohols Methanol Ethanol 23.6 -95 -26.2 3532. Degler & Miles.8 -94.497 47.0 3491.0 12.1 100.564 44.544 49. Napthenes CnH2n Cyclopentane 17.4 173.1 84.5 57.6 3632.002 0 32.785 47.6 43.8 -185 -195 -137.424 0.2 -0.1 -97.4 Boiling Temp.87 0.1 280 307.8 ……… 3558.03 290.143 44.0 …….5 94.596 44. ……….497 ……… 47.3 170.0 46.778 51.998 …… …… …… 1.8 -47. ……… 10.546 0.692 0.6 80. (4 ml TEL/gal.303 45.5 62.0 18.725 29.1 106.7 5.27 1167.317 40.625 0.6 110.792 46. Alcohols 22.450 48. and Gas PowerFamily Name SIT++ oC 730 566 535 516 501 478 …… 732 463 …… …… …… …… …… …… …… …… 739 811 …… …… …… …… …… …… …… …… 609 …… 0.7 Latent Heat.7 -135 -129..1 99. Olefins CnH2n Hexene-1 15.675 0.4 245.2 142. oC -182.7 3688.111 0.582 0.3 -42.) Rich Leana …… …… …… …… …… …… …… …… 63 63 0b 0b 200 360 153 153 …… …… …… …… …… …… …… …… …… …… 84 …… …… …… 100 >160 Mol.5 …….I.2 100.547 39.9 ……… ……… ……… ……… ……… ……… 362.2 -172.2.44 ……….1 ……… 0 ………. Gas CnH2n+2 Methane Ethane 2. Air & Gas Power by Severns.75 297.4 -90.36 Team.. Gasoline CnH2n+2n n-Heptane 7.0 142. LPG CnH2n+2n Pentane 6.1 110a 104a 100 92 61 0 …….358 49.241 45.782 0. 73.2 114.la Melting Temp. Fuel Oil CnH2n+2 Decane 10.86 393. Gasoline CnH2n+2n Triptane 8.1 3550.235 47.4 3625.0 42.3 3595.88 0.008 41.8 -6.612 40..566 43.5 42.3 3494.583 45. 100 …….031 0.4 130 >160 >160 …… >180 >180 …… …… …… …… 93 …… API Gravit y 202.984 40.8 3591.2 32.0 31.1 70.310 43.111 3506.746 55.564 44.730 0. ……….570 0.79 374.1 …… …… …… …… …… …… 0.6 140. Fuel Oil CnH2n+2n Octadecane 13.88 ……… ……….0 1.682 50.56 36.5 3439.2 3599. 5th ed. John Wiley.348 44. Fuel Oil CnH2n+2n Dodecane 11. ……….1 84.3 226.427 44.9 3506. Abstracted from Table V Properties of Hydrocarbons of Steam.0 56..0 44. 388. Naphthenes CnH2n Cyclohexane 18.726 ……….73 251..0 31.10 169.909 46..2 -186.555 46. 16.0 30.7 63.991 ………….5 3614.21 248.869 47. 100 …… 85 82 84.846 48.916 47.2 -136.5 75. Gasoline CnH2n+2n Iso-Octane 9.5 194.653 0.1 72.475 52.2 3610. 28.0 …… 76. Carbon monoxide Gas Turbines . C6H6 C7H8 C8H10 CH3O H C2H6O C8H20P b H2 H2O C …….671 44..0 116.684 0. 1964. Gasoline (straight run) 28.8 65 80. Hydrogen (gas) 25. CO 24.079 48.626 0.705 20. Fuel Oil CnH2n+2n Hexadecane 12. Carbon (solid) 27.. LPG CnH2n+2n Butane 5.5 51.102 50.44 383. Olefins CnH2n 16. Aromatics CnH2n-6 Benzene 19.85 407.09 362.1 98. less flammable and generally safer to store and transport. but typically use fuels with much higher flash points. It is usually a high-octane gasoline known as “avgas”. Most jet fuels are basically kerosene-based. The open air burning temperature in Table 4-2 can be compared with the typical distillation characteristics for aircraft gas turbine fuel in Fig. The aviation gasoline graph at the bottom of the graph is for piston-engine powered aircraft and it has a low flash point to improve its ignition characteristics. Degree Centigrade scale supplied by Prof. Relative to the “pure substance” single evaporation temperatures of water and ethyl alcohol. gasoline is a mixture of liquid several hydrocarbons and its various components boil off at different temperatures as can be seen in the graphs. and Gas Power by Severns. making them safer to handle than the traditional avgas.1. R. Degler & Miles. Turbine engines on the other hand can operate with a wide range of fuels. 4. ‘Layi Fagbenle. 4-1. 1964.Exergy and Environmental Considerations in Gas Turbine Technology and Applications 37 Fig. Abstracted from Steam. . Typical ASTM distillation characteristics for various types of fuels. 4-1 below shows typical distillation characteristics for military and commercial aircraft fuels. Both the Jet A specification fuel used in the USA and the Jet A-1 standard specification of most of the rest of the world have a relatively high flash point of 38°C and a self-ignition temperature (SIT) (or auto-ignition temperature) of 210°C. Air. Fig. John Wiley & Sons Inc. Typical Specifications for Jet A and Jet A-1 Aircraft Fuels (from Wikipedia) Specifications for Heavy-Duty Gas Turbine Fuels Heavy-duty gas turbines are able to burn a wide range of gaseous fuels and hence are less restricted in their fuel classifications.50 7. Other process gases used as gas turbine fuels are byproducts of steel production such as blast furnace gases and coke oven gases. sulfur (as H2S or COS). allowable gas fuel contaminant levels are also specified for such trace metals as (Pb. Butane CO.38 Physical Properties Flash Point Self. The feedstock for gasification fuels can be coal.81 – 7. H2. Sodium (Na) is the only trace metal contaminant normally found in natural gas. and the fuel.2. petroleum coke or heavy liquids.4 °F) 210 °C (410 °F) < -47 °C (-52. liquid (water and/or hydrocarbon) condensates and lubricating oils from compressor stations. and it source is salt water in the ground gas wells. Blast Furnace Gases (BFG) have heating values below minimal allowable limits for gas turbine fuels. Range of typical heavy-duty gas turbine fuel classification (adapted from GEI 41040G – GE Gas Power Systems.90 11. steam and water for injection. CO2 Table 4. Ca. Sources of contaminants in heavy-duty gas turbine applications include particulates arising largely from corrosion chemical reactions in gas pipelines. Revised January 2002).70 – 119.775 kg/l – 0. and CO2. Alkali metals (Na and K) and particulates.5 °F) 0.73 – 5.30 Major Components Methane Propane. and Mg). H2. natural gas or hydrocarbons such as propane or butane. H20v CH4.3. Constituents of process gases include CH4.840 kg/l > 42.80 MJ/kg Table 4. CO. In addition to such specifications which may be particular to each turbine manufacturer. necessitating blending with other fuels such as coke oven gas. H2. . N. alkali metals contained in compressor discharge. Fuel Natural Gas and Liquefied Natural Gas (LNG) Liquefied Petroleum Gas [LPG] Gasification Gases (Air Blown) Gasification Gases (Oxygen Blown) Process Gases LHV [MJ/m3] 29.20 – 37. H20v CO. CO.23 3. V.5 °C (549. trace metals. for example refinery gases). Typical gas turbine fuel specification ranges appear in Table 4-4 below.45 85.(auto-) ignition temperature Freezing point Open air burning temperature Density (per litre) Specific energy (calorific value) Jet A-1 Gas Turbines Jet A > 38°C (100.45 – 14. Process gases are generated by many petrochemical and chemical processes and are suitable for fuelling gas turbines. Gasification fuels generally have lower much lower heating values than other fuel gases.6 °F) < -40 °C (-40 °F) 287. H2. and they are produced by one of two processes: oxygen blown or air blown gasification process. A typical heavy-duty gas turbine fuel specification (range only indicated) appears in Table 4-3 below. Conventional and New Environmental-conscious Aero and Industrial Gas Turbine Fuels Conventional aero gas turbine fuels are commonly: i. or any other hydrocarbon feedstock (e.g. lignocellulosic biomass and other agricultural wastes used as feed into the FTS (2nd generation biofuels) to produce liquid fuels (FTL). ii.Range within limits Flammability Ratio Constituent Limits. mole % Methane. Max None 54 +5% Min 3. camelina. etc.) Sulfur C6H6. These are produced by first gasifying the hydrocarbon resource followed by liquefaction to form hydrocarbon liquids (e. shale. Revised January 2002).. as well as animal fats. Bio-ethanol and bio-methanol neat or mixed in regulated proportions with gasoline. CO Oxygen. Bio-syngas produced by gasification of biomass. tar sands. Methane and Hydrogen.73 –11. volume basis % of reactant species % of reactant species % of reactant species % of reactant species % of reactant species % of reactant species % of reactant species % of reactant species % of total (reactants + inerts) 100 15 15 5 Trace Trace Trace Trace 15 Report Report 85 0 0 0 0 0 0 0 0 0 0 Table 4. and ii. Kerosene from crude petroleum sources using established refining processes. the Airline Industry Information update dateline 26 June 2009) New Environmentally-conscious aero gas turbine fuels are: i. Bio-fuels from bio-derived Fatty Acid Methyl Esters (FAME) mixed with conventional aero fuel (kerosene) in regulated proportions. palm oil. soybeans. iii. iv. CH4 Ethane. Liquefied gases such as LNG.).Absolute limits .20 40 -5% 2.5 below gives relative properties of conventional aviation kerosene and typical biodiesel aircraft fuel (will vary with Fatty Acid Methyl Esters [FAME] type): . Both methane and hydrogen will have to be liquefied for use as aircraft fuel. Range of typical heavy-duty gas turbine fuel specification (adapted from GER 41040G – GE Gas Power Systems. sunflower. rapeseed (canola). Liquefied petroleum gas (LPG) which is really not a cryogen.4. and v.Exergy and Environmental Considerations in Gas Turbine Technology and Applications 39 Fuel Properties Lower Heating Value. H2 Carbon monoxide. C2H6 Propane. etc. C3H8 Butane C4H10 + higher paraffins (C4+) Hydrogen.g. Table 4. natural gas. synthetic kerosene from Fischer-Tropsch (FT) synthesis using coal. O2 Total Inerts (N2+CO2+Ar) Aromatics (Benzene Toluene C7H8. etc. as earlier noted. Biofuels produced from Fischer-Tropsch Synthesis (FTS) process using biomass feedstock such as oil seeds – jathropha.2:1 Notes Rich:Lean Fuel/Air Ratio. MJ/m3 Modified Wobbe Index (MWI) . 6. Table 4. It is a gas rich in carbon monoxide and hydrogen with typical composition shown in Table 4.4 (spec. titled “A Gas Turbine Manufacturer’s View of Biofuels”. etc. Balat et al. Presentation by Chris Lewis.015 Excluded Excluded Controlled to well defined level Hydrocarbon C16 – C22 >101 -3? 0 10 0. Material compatibility Hot-end life Hot-end life Fuel system & injector life Elastomer compatibility From: Ppt. (dry & N2-free) 28 – 36 22 – 32 21 – 30 8 – 11 2–4 0. Typical composition of bio-syngas from biomass gasification.96 0.°C max Sulfur [ppm] max Acidity [mg KOH/g] max Phosphorous [ppm] max Metals [ppm] max Thermal Stability Composition C14 – C15 max (trace levels) 38 -47 3000 0. Rolls Royce plc.2 775 – 840 Bio-diesel 32 – 39 860 – 900 20% Blend 41. min: 42. sewage sludge. 2006.16 – 0. limits. In the steam-reforming reaction. paper mill sludge. agricultural biomass wastes and lignocellulosic plants) to produce bio-syngas. biomass. Carbon length Flash point. .0 – 42.021 Source: M.5 10 5 Not controlled FAME 0. H2S.84 – 0. Cold Start and Relight. Freeze Point. black liquor.8) 792 – 852 Gas Turbines Impact Airframe range/loading Wing tank temp. Cold Starts & Relight.) % by vol. waste oil. °C min. limits.22 0. Constituents Carbon monoxide (CO) Hydrogen (H2) Carbon dioxide (CO2) Methane (CH4) Ethene (C2H4) Benzene-Toluene-Xylene (BTX) Ethane (C2H5) Tar Others (NH3. steam reacts with feedstock (hydrocarbons. Approx. Company Specialist – Fluids. ash.24 < 0.15 – 0.6 below. refusederived fuel. dust. Combustion emissions Wing tank temp.40 Property Heat of combustion [MJ/kg] typical Density [kg/m3] range Viscosity [mm2/sec @ -20°C max. municipal organic waste. Energy Conversion and Management 50 (2009) 3158 – 3168).11 2 1 Not known 20% FAME C16 – C22 Unchanged -5 to -10 with additives Aviation Kerosene 43. HCl. Proceedings of the Combustion Institute. Gas Turbines and Biodiesels A recent study by Bolszo and McDonnell (2009)1 on emissions optimization of a biodieselfired 30-kW gas turbine indicates that biodiesel fluid properties result in inferior atomization and longer evaporation times compared to hydrocarbon diesel. G. D. The results showed that petroleum diesel fuels tend to generate the highest temperatures while natural gas has the lowest. Pages 2949-2956. 2 Pierre A. It was found that the minimum NOx emission levels achieved for biodiesel exceeded the minimum attained for diesel. the lab test showing a higher NOx emission while the two field tests showed slightly lower NOx emission relative to petroleum diesel. It is however clear that biodiesels have reduced carbon-containing emissions and there is agreement also on experimental data from diesel engines which indicate a slight increase in NOx relative to petroleum diesel. Bolszo and V. (2009). Issue 2. McDonell. Glaude. Vol 32. Factors limiting gas turbine performance The Joule cycle (also popularly known as the Brayton cycle) is the ideal gas turbine cycle against which the performance (i. Premixed. Ethanol-powered gas turbines for electricity generation In a 2008 report by Xavier Navarro (RSS feed). We prefer to restrict the use of Joule 1 C. palm and tallow. It was also claimed that the combustion of the bio-derived ethanol produced virtually no net CO2 emissions. one carried out in Europe on rapeseed methyl ester (RME) and the other in USA on soybean methyl ester (SME). The five FAME’s studied by Glaude et al. SME. the thermal efficiency of the cycle ηCY) of an actual gas turbine cycle is judged under comparable conditions. Gasoil and Natural Gas. a company called LPP Combustion (Lean. 5.e. were RME. with biodiesel lying in-between. A theoretical study was recently carried out by Glaude et al. SO2 and PM (soot) from biofuel ethanol (ASTM D-4806) were the same as natural gas-level emissions achieved using dry low emission (DLE) gas turbine technology. 2009. CO.Exergy and Environmental Considerations in Gas Turbine Technology and Applications 41 A useful reference for the thermo-conversion of biomass into fuels and chemicals can be found in the above referenced paper by M. This ranking thus agrees with the two field tests mentioned earlier. Gas Turbines and Biodiesel: A clarification of the relative NOx indices of FAME. emissions of NOx. Emissions optimization of a biodiesel fired gas turbine. and methyl esters from sunflower. and that optimizing the fuel injection process will improve the biodiesel NOx emissions. The study was necessitated by the conflicting results from a lab test on a microturbine and two recent gas turbine field tests. It was also found out that the variability of the composition of petroleum diesel fuels can substantially affect the adiabatic flame temperature. Roda Bounaceur and Michel Moliere. Rene Fournet. (2009)2 to clarify the NOx index of biodiesels in gas turbines taking conventional petroleum gasoils and natural gas as reference fuels. Prevaporized) was claimed to have demonstrated that during gas turbine testing. Balat et al. . while biofuels are less sensitive to composition variations. The adiabatic flame temperature Tf was considered as the major determinant of NOx emissions in gas turbines and used as a criterion for NOx emission. From Haywood [ ].42 Gas Turbines cycle to the ideal gas turbine cycle while the Brayton cycle is exclusively used for the actual gas turbine cycle.1) Hence. as the area of the cycle on the T-s and p-V diagrams indicate. Fig. Thus. 5. 5.1 above for Ta = 15°C and Tb = 100°C as shown in Fig. Haywood considers an interesting graphical representation of eq. which occurs when the temperature after isentropic compression from Ta is equal to the TIT Tb. the net work done is seen to be equal to zero. The ideal gas turbine “closed”cycle (or Joule cycle) consists of four ideal processes – two isentropic and two isobaric processes – which appear as shown in Fig. the thermal efficiency of the ideal gas Joule cycle is a function only of the pressure ratio. the cycle is referred to as the air-standard Joule cycle. If air is the working fluid employed in the ideal Joule cycle. when this occurs. Since for isentropic processes 1-2 and 3-4. However. 5. = T3 T4 = ρ p . Fixing the inlet temperature to the compressor Ta and the inlet temperature to the turbine Tb automatically sets a limit to the pressure ratio rp.1.1. ρp is essentially the isentropic temperature ratio.1. The thermal efficiency of the Joule cycle in terms of the pressure ratio rp given by ( rp = p B and the pressure ratio parameter ρp given by ρ p = rpγ − 1)/γ is: A p ⎛ ⎞ ⎛ 1 1 ⎞ ⎟ η Joule = ⎜ 1 − (γ −1)/γ ⎟ = ⎜ 1 − ⎜ ⎟ ⎜ ρp ⎟ rp ⎝ ⎠ ⎝ ⎠ T2 T1 (5. 5. Ideal Joule cycle (a) p-V and (b) T-s state diagrams. the abscissa in Fig. but independent of the compressor and the turbine inlet temperatures separately without a knowledge of the pressure ratio. 5.2 . the Joule efficiency is also dependent of the isentropic temperature ratios only. Variation of cycle efficiency with Isentropic temperature ratio ρp (ta = 15°C). wherein the heat and work terms in each of the processes are identified. a sketch of the Joule cycle on the T-s diagram shows that as rp approaches this value. In Fig. ta = 15°C for two values of tb = 800°C and 500°C respectively. is now much larger than its previous value for the ideal Joule cycle while the turbine work output WT is considerably smaller than for the ideal Joule cycle.2.2 for tb = 800°C. ignoring the frictional effects in the heat exchangers. However. An analytic expression for the Brayton cycle thermal efficiency can be shown to be: ηBrayton = (1 − 1 / ρ p )(α − ρ p ) (β − ρp ) (5. revealing the considerable effect of turbine and compressor inefficiencies on the cycle thermal efficiency. to which the remaining two curves in the graph pertain. 5. and to only 4. β = [1 + ηC(θ – 1)]. The h-s curve diagram for such a gas turbine Brayton cycle appears in Fig. the area enclosed by the cycle approaches zero. showing a drastic reduction from TIT = 800°C to TIT = 500°C.82 approximated to 100 in the figure is attained when ρp = θ = Tb/Ta = 1073/288 = 3. 5. The optimum pressure ratio is now reduced from approximately 100 to 11.8 at tb = 500°C. the actual Brayton cycle performance is depicted for turbine and compressor isentropic efficiencies of 88% and 85% respectively.2) where α = ηCηTθ. This optimum pressure ratio is more realistically achievable in a single compressor. ductings and combustion chamber. Here also. 5. . We note that the compressor work input required WC. we find that ηBrayton is highly dependent on θ = Tb/Ta. ηJoule increases continuously with rp right up to the limiting value as the curve labeled “reversible” shows.3. 5.7257. a pressure ratio this large is never used when issues of process irreversiblities are considered. and θ = Tb/Ta. Fig. In practical terms. From Haywood [ ]. frictional effects in turbines and compressors and pressure drops in heat exchangers and ductings and combustion chamber are basically lost opportunities for production of useful work.1 Effect of irreversibilities in the actual gas turbine cycle In an actual plant. Under this condition.Exergy and Environmental Considerations in Gas Turbine Technology and Applications 43 For Ta = 15°C and Tb = 100°C.2. The limiting pressure ratio rp = 99. 44 Gas Turbines The compressor work input per unit mass of working fluid is c pTa Wc = c p (T2′ − Ta ) = ( ρ p − 1) (5. and Wnet with isentropic temperature ratio ρp. It may also be shown that.r.3) ηc while ⎛ 1 ⎞ ′ WT = c p (Tb − T4 ) = c pηT Tb ⎜ 1 − ρ ⎟ (5. From Haywood [ ]. compressor work input WC. 5. From 5. The method indicates that the points of maximum thermal efficiency of the Brayton cycle ηCY and the maximum Wnet are not coincident. Enthalpy-entropy diagram for Actual Brayton cycle. Variation of heat supplied to the combustor QB. The maximum efficiency is obtained at the value of ρp corresponding to the point H at which a straight line from point E is tangent to the curve for Wnet. rather the value of ρp is greater for the former than for the latter. WT.5) ⎠ ηc ⎝ with α = ηCηTθ and θ = Tb/Ta as before. and Wnet with variation in ρp for fixed values of Ta and Tb. with turbine and Compressor inefficiencies. The variation of Wnet with the adiabatic temperature ratio ρp appears in Fig.t. i.e at ρp = ρopt.4. Also from differentiating 5.4 due to Hawthorne and Davis [ ] for the variation of QB. ρp. then ρ w = (1 − ηm ) opt where ηm is the maximum value of the thermal efficiency of the Brayton cycle. we obtain that Wnet is maximum when ρp = √α. turbine work output WT.4. ρ . Wnet vanishes when ρp = 1 and when ρp = α.4) p ⎠ ⎝ and Wnet = ( WT – WC ) = c pTa ⎛ 1 ⎞ ⎜ 1 − ρ p ⎟ (α − ρ p ) (5. Haywood [] discusses the graphical construction in Fig. Fig. 5. 5. if ρW and ρopt are the values of ρp for maximum Wnet and maximum ηCY respectively. 5.3. Fig. WC.5 w. From Haywood [ ].5. Exergy and Environmental Considerations in Gas Turbine Technology and Applications 45 Figs. 5.5 and 5.6 show the schematic of the simple-cycle, open-flow gas turbine with a single shaft and double shaft respectively. The single shaft units are typically used in applications requiring relatively uniform speed such as generator drives while in the dual shaft applications, the power turbine rotor is mechanically separate from the high-pressure turbine and compressor rotor. It is thus aerodynamically coupled, making it suitable for variable speeds applications. Fig. 5.5. Simple-cycle, open-flow, single-shaft gas turbine Fig. 5.6. Simple cycle, open-flow, dual-shaft gas turbine for mechanical drives. 5.2 Simple-cycle vs. Combined-cycle gas turbine power plant characteristics Fig. 5.7 shows the variation of output per unit mass and efficiency for different firing temperatures and pressure ratios for both simple-cycle and combined-cycle applications. In the simple-cycle top figure, at a given firing temperature, an increase in pressure ratio results in significant gains in thermal efficiency. The pressure ratio resulting in maximum efficiency and maximum output are a function of the firing temperature; the higher the pressure ratio, the greater the benefits from increased firing temperature. At a given 46 Gas Turbines pressure ratio, increasing the firing temperature results in increased power output, although this is achieved with a loss in efficiency mainly due to increase in cooling air losses for aircooled nozzle blades. On the other hand, pressure ratio increases do not affect efficiency markedly as in simplecycle plants; indeed, pressure ratio increases are accompanied by decreases in specific power output. Increases in firing temperature result in marked increases in thermal efficiency. While simple-cycle efficiency is readily achieved with high pressure ratios, combined-cycle efficiency is obtained with a combination of modest pressure ratios and higher firing temperatures. A typical combined-cycle gas turbine as shown in Fig. 5.7 (lower cycle) will convert 30% to 40% of the fuel input into shaft output and up to 98% of the remainder goes into exhaust heat which is recovered in the Heat Recovery Steam Generator (HRSG). The HRSG is basically a heat exchanger which provides steam for the steam turbine part of the combined-cycle. It is not unusual to utilize more than 80% of the fuel input in a combined-cycle power plant which also produces process steam for on- or off-site purposes. Fig. 5.7. Gas turbine characteristics for simple-cycle (above) and for combined-cycle (below). Abstracted from GE Power Systems.GER-3567H 10/00. 5.3 Other factors affecting gas turbine performance Other factors affecting the performance of a gas turbine (heat rate, power output) include the following: Air temperature (compressor inlet temperature) and pressure; Site elevation or altitude; humidity; inlet and exhaust losses resulting from equipment add-ons such as air filters, evaporative coolers, silencers, etc. The usual reference conditions stated by manufacturers are 59F/15C and 14.7 psia/1.013 bar. In general, output decreases with increasing air temperature while the heat rate increases less steeply. Similarly, altitude Exergy and Environmental Considerations in Gas Turbine Technology and Applications 47 corrections are provided by manufacturers with factors less than 1.0 at higher latitudes. The density of humid air is less than that of dry air and it affects both the heat rate and the specific output of a gas turbine. The higher the humidity, the lower the power output and conversely the higher the heat rate. Inlet and exhaust pressure losses result in power output loss, heat rate increase and exhaust temperature increase. 5.4 Gas turbine emissions and control Over the past three to four decades, many developed countries have put in place applicable state and federal environmental regulations to control emissions from aero, industrial and marine gas turbines. This was the case even before the current global awareness to the Climate Change problem. Only NOx gas turbine emission was initially regulated in the early 1970s and it was found that injection of water or steam into the combustion zone of the combustor liner did produce the then required low levels of NOx reduction without serious detrimental effects on the gas turbine parts lives or the overall gas turbine cycle performance. However, as more stringent requirements emerged with time, further increase in water/steam approach began to have significant detrimental effects on the gas turbine parts lives and cycle performance, as well increased levels of other emissions besides NOx. Alternative or complimentary methods of emission controls have therefore been sought, some internal to, and others external to, the gas turbine, namely: i. Dry Low NOx Emission (DLN) or DLE burner technology ii. Exhaust catalytic combustion technology iii. Overspray fogging While NOx emissions normally include Nitrous oxide (NO) and Nitrogen dioxide (NO2), NOx from gas turbines is predominantly NO, although NO2 is generally used as the mass reference for reporting NOx. This can be seen from the typical exhaust emissions from a stationary industrial gas turbine appearing in Table 5.1. Table 5.1. Typical exhaust emissions from a stationary industrial gas turbine. Abstracted from GE Power Systems – GER-4211-03/01. 48 Gas Turbines NOx are divided into two main classes depending on their mechanism of formation. NOx formed from the oxidation of free nitrogen in either the combustion air of the fuel are known as “thermal NOx”, and they are basically a function of the stoichiometric adiabatic flame temperature of the fuel. Emissions arising from oxidation of organically bound nitrogen in the fuel (the fuel-bound-nitrogen, FBN) are known as “organic NOx”. Of the two, efficiency of conversion of FBN to NOx proceeds much more efficiently than that of thermal NOx. Fig. 5.8. Typical NOx emissions for a class of Industrial gas turbines. Abstracted from GE Power Systems – GER-4311-03/01. Fig. 5.9. Typical NOx emissions for a class of Industrial gas turbines. Abstracted from GE Power Systems – GER-4311-03/01. Thermal NOx is relatively well studied and understood, but much less so for organic NOx formation. For thermal NOx production, NOx increases exponentially with combustor inlet air temperature, increases quite strongly with F/A ratio or with firing temperature, and increases with increasing residence time in the flame zone. It however decreases exponentially with increasing water or steam injection or increasing specific humidity. Figs. Exergy and Environmental Considerations in Gas Turbine Technology and Applications 49 5.1 and 5.2 show typical NOx emissions for industrial gas turbines operating on natural gas fuel and No.2 distillate as a function of firing temperature. As regards organic NOx, reduction of flame temperature (as through water or steam injection) does scant little to abate it. Water and steam injection are known to actually increase organic NOx in liquid fuels. As noted earlier, organic NOx is important only for fuels containing significant amount of FBN such as crude or residual oils. Carbon Monoxide (CO) emissions as seen from Table 5.1 can be of comparable magnitude with NO emission, depending on the fuel and the loading condition of the gas turbine. Fig. 5.10 is a typical industrial gas turbine CO emission as a function of firing temperature. We note that, contrary to the NOx trend, CO emission increases significantly as the firing temperature is reduced below about 816°C (1500°F). It is noted that carbon monoxide is normally expected from incomplete combustion and hence inefficiency in the combustion process. Fig. 5.10. CO emissions from an industrial gas turbine. Abstracted from GE Power Systems – GER-4311-03/01. Fig. 5.11. UHC emissions from an industrial gas turbine. Abstracted from GE Power Systems – GER-4311-03/01. 50 Gas Turbines Unburned hydrocarbons (UHC) are also products of the inefficiency in the combustion process. Fig. 5.11 shows a typical industrial gas turbine UHC emission as a function of firing temperature. Particulates. Fuel properties, combustor operating conditions and the design of the combustor all affect the gas turbine exhaust particulate emission, whose main components are smoke, ash, erosion and corrosion products in the metallic ducting and piping of the system. Gas Turbine Emission Control Techniques Emission NOx CO UHC & VOC SOx Particulates & PM-10 Smoke Control technique Lean Head End Liner; Water or Steam Injection; Dry Low NOx Emission (DLE); Overspray fogging Combustor Design; Catalytic reduction Combustor Design Control of sulfur in fuel Fuel composition influencing Sulfur & Ash; Combustor design; Fuel composition; Air atomization 6. Exergy considerations Publication of research articles on exergy consideration in power cycles dates back about four decades now, possibly with the initial work of Kalina (1984) on the combined cycle system with novel bottoming cycle and that of El-Sayed and Tribus (1985) on a theoretical comparison of the Rankine and Kalina cycles. This was followed with the work of Zheng et al. (1986a) on Energy Utilization Diagram (EUD) for two types of LNG power-generation systems; Zheng (1986b) on graphic exergy analysis for coal gasification-combined power cycle based on EUD; Ishida et al. (1987) on evaluation of a chemical-looping-combustion power-generation system by graphic exergy analysis; and Wall et al. (1989) ending the first decade with an exergy study of the Kalina cycle that began the decade. In the second decade belong the works of Najjar (1990) on hydrogen fuelled and cooled gas turbines; Ishida et al. (1992a) on graphic exergy analysis of fuel-cell systems based on EUDs; Jin & Ishida (1993) on graphical analysis of complex cycles; Joshi et al. (1996) on a review of IGCC technology; and Jaber et al. (1998) on gaseous fuels (derived from oil shale) for heavyduty gas turbines and Combined Cycle Gas Turbines. The third decade began with the analysis of Bilgen (2000) on exergetic and engineering analysis of gas turbine-based cogeneration systems; Thongchai et al. (2001) on simplification of power cycles with EUDs; Marrero et al. (2002) on 2nd law analysis and optimization of a combined triple power cycle; Jin & Ishida (2004) on graphic presentation of exergy loss in mixing on an EUD; Khaliq (2004) on second-law analysis of the Brayton/Rankine combined power cycle with reheat; Khaliq (2004b) on thermodynamic performance evaluation of combustion gas turbine cogeneration systems with reheat; Ertesvag et al. (2005) on exergy analysis of a gas turbine combined cycle power plant with pre-combustion CO2 capture; Tae won Song et al. (2006) on performance characteristics of a MW-class SOFC/GT hybrid system based on a commercially available gas turbine; Guillermo Ordorica-Garcia et al. (2006) on technoeconomic evaluation of IGCC power plants for CO2 avoidance; Fagbenle et Exergy and Environmental Considerations in Gas Turbine Technology and Applications 51 al (2007) on thermodynamic analysis of biogas-fired integrated gasification steam-injected gas turbine (BIG/STIG) plant; Karellas et al. (2008) on thermodynamic evaluation of combined cycle plants; Fadok et al. (2008) on an update on advanced hydrogen turbine development; Bartieri et al. (2008) on biomass as an energy resource – the thermodynamic constraints on the performance of the conversion process in producing synthetic gas (syngas) for high efficiency internal combustion engines such as CCGT as well as in fuel cells (MCFC and SOFC) after adequate cleaning up and reforming; Khaliq (2009a) on exergy analysis of a gas turbine trigeneration system for combined production of power, heat and refrigeration; Khaliq (2009b) on energy and exergy analyses of compression inlet air-cooled gas turbines using the Joule-Brayton refrigeration cycle; Khaliq (2009c) on exergy analysis of the regenerative gas turbine cycle using absorption inlet cooling and evaporative aftercooling; Farzaneh-Gord et al. (2009) on a new approach for enhancing performance of a gas turbine using as a case study the Khangiran refinery in Iran; Fachina (2009) on Exergy accounting – the energy that matters; and finally closing the highly productive decade with Baratieri et al. (2009) on the use of syngas in IC engines and CCGT. The fourth decade has begun with Woudstra et al. (2010) on thermodynamic evaluation of combined cycle plants. This does in no way claim to be a complete account of all the contributions to exergy analyses of power cycles from inception to the present time, rather we have tried to give some highlights on the journey so far. Exergetic Analyses of Power Cycles – Gas Turbines, CCGTs, IGCC & BIG/STIG Dincer and Rosen (2007) have listed the following benefits of using exergy analysis in industrial plant equipment and processes: Efficiencies based on exergy, unlike those based on energy, are always measures of the • approach to true ideality, and therefore provide more meaningful information when assessing the performance of energy systems. Also, exergy losses clearly identify the locations, causes and sources of deviations from ideality in a system. • In complex systems with multiple products (e.g., cogeneration and trigeneration plants), exergy methods can help evaluate the thermodynamic values of the product energy forms, even though they normally exhibit radically different characteristics. • Exergy-based methods have evolved that can help in design-related activities. For example, some methods (e.g., exergoeconomics and thermoeconomics) can be used to improve economic evaluations. Other methods (e.g., environomics) can assist in environmental assessments. • Exergy can improve understanding of terms like energy conservation and energy crisis, facilitating better responses to problems. The following table comparing energy and exergy from Dincer & Cengel [ ] is also useful in appreciating exergy. According to Szargut et al. [1988], “exergy is the amount of work obtainable when some matter is brought to a state of thermodynamic equilibrium with the common components of the natural surroundings by means of reversible processes, involving interaction only with the above mentioned components of nature”. Four different types of exergy are identifiable in principle, denoted as kinetic, potential, physical and chemical exergy, Masim and Ayres [ ], viz.: ε = εk + εp + εph + εch Chemical exergy is the work that can be obtained by bringing a substance having the temperature and pressure (T. Is always conserved in a reversible process. a measure of the “distinguishability” of the target system from its environment.p). Consideration of physical exergy is important for optimization of thermal and mechanical processes including heat engines and power plants. and independent of the environment parameters. Physical exergy is the work obtainable by taking a substance through reversible physical processes from its initial state at temperature T and pressure p to the final state determined by the temperature To and pressure po of the environment. EXERGY Is dependent on both the parameters of matter or energy flow and on the environment parameters. or alternatively. Is a measure of quantity and quality due to entropy. Is motion or ability to produce motion. Has the values different from zero (equal to mc2 upon Einstein’s equation) Is governed by the 1st Law of Thermodynamics (FLT) for all the processes. Is governed by the 1st Law of Thermodynamics (FLT) for reversible processes only (while it is destroyed partly or completely in irreversible processes). the exergy (loss) Δε is given by: Δε = B = S(T-To) – V(p-po) + ∑μi(Ni – Nio) . Wk and Wp. Is a measure of quantity only. more appropriately. the analytical expression for exergy shows that exergy is a measure of the “thermodynamic distance” of the target system from equilibrium. As Masim and Ayres [ ] put it. Hence the importance of defining a reference state when calculating both physical and chemical exergy. both of which are usually negligible in the analysis of most common industrial processes. Is work or ability to produce work. It has two components – one associated with chemical reactions occurring in isolation. [1988]. Kinetic and potential exergy (εk & εp) have the same meaning as their corresponding energy or work terms. Is not limited for reversible processes due to the 2nd Law of Thermodynamics (SLT). such as chemical and metallurgical processes. but is always consumed in an irreversible process. namely the state of the “target” system and that of its surroundings (or. it is of secondary importance and often negligible when attention is focused on very large systems. the ultimate state of the combined system plus its surroundings. Szargut et al.52 Gas Turbines ENERGY Is dependent on the parameters of matter or energy flow only. so can neither be destroyed or produced. and the other associated with the diffusion of reaction products into the surroundings. Is limited by the 2nd Law of Thermodynamics (SLT) for all processes (including reversible ones). For a closed system with (T.1. Table 6. where chemical exergy dominates in resource accounting and environmental analyses Masim and Ayres [ ]. Masim and Ayres [ ]. and chemical composition μo). Is always conserved in a process.p) to a state of thermodynamic equilibrium with the datum level components of the environment. after they have reached mutual equilibrium of pressure po. temperature To. Is equal to zero (in dead state by equilibrium with the environment). The exergy function is thus a measure of the difference between two states. However. appropriately. Exergetic Analyses of Gas Turbine Cogeneration/Combined Cycle Plants The generic name “Cogeneration or Combined Cycle” plants is used for gas turbine top cycle plant whose hot exhaust is used for generating steam in a heat recovery steam generator (HRSG) for a steam turbine bottom cycle. it could be any power plant that generates “waste” heat from which we are able to extract “useful” thermal energy. the fuel is thus not produced on-site. However.1. Δε ≤ 0. . As noted earlier.1. The gas turbine exhaust gases produce the steam in the HRSG. the ambient atmospheric pressure and temperature respectively.C. they may also generate both power and steam from the steam turbine if process steam is required on-site or elsewhere. 6. many CHP plants are powered by large diesel Internal Combustion (I. the gas turbine combustion chamber (combustor) is fuelled normally with liquid or gaseous fuels piped to the plant from nearby storage tanks. the Cogeneration/CC plant would properly qualify to be called a Combined Heat and Power (CHP) Plant.3). In this case. although this appellation is technically reserved for any power plant whose hot combustion product gases are used to generate steam for on-site or other uses. Fig.To(S-So) . it is important to have a knowledge of the detailed average chemical composition of the reaction products and the environmental sink with which the system reacts Masim and Ayres [ ].Exergy and Environmental Considerations in Gas Turbine Technology and Applications 53 where Ni is the number of moles of the ith system and μi is its chemical potential. Δε = B = (H – Ho) . From Bilgen (2000).) engines. as in district heating systems. the equality holding only when the process is reversible. We first consider the work of Bilgen (2000) on exergetic analyses of gas turbine cogeneration systems in which gas turbine cogeneration systems involving three different combinations of power and steam generation from a gas turbine and a steam turbine fed with steam from a HRSG were studied (see Figures 6. In this regard. Here po and To are. Thus a CHP need not have a gas turbine in its power production train.∑μi(Ni – Nio) where H is enthalpy. For a flow or open system.2 and 6. where mass crosses the system boundaries. In these plants. 6. Cogeneration/Combined Cycle plants therefore generate additional power from the steam turbine. In such a case. 3.54 Gas Turbines Fig. using Lagrangian multipliers.2. 6. The second law or exergy efficiency is defined as ε= ( We + Bp ) Bf (6.1) Where Ef is the energy of the fuel. The fuel utilization efficiency or the 1st Law efficiency is given by η =C ( W e + Qp ) Ef (6. Bilgen undertook a combustion analysis by calculating the composition of the fuel gas mixture using direct minimization of the Gibbs function of formation of each compound I from its constituent elements. 6.2) .98 as the parasitic system loss is assumed to be 2%. We and Qp are the electrical energy and the thermal energy of the process respectively while C is 0. From Bilgen (2000). From Bilgen (2000) Fig. and To is temperature of the environment.2 for base-load gas turbine at ISO conditions of 288 K and 101. sc is the entropy of the condensate return. η.9) Two Case Studies corresponding to Figures 6. and the pinch point temperature difference is 50 K.b) A relationship can be established between exergy. Qp = ms(h-hc) Process heat exergy factor and power-to-heat ratio are defined as (6. Bp is the exergy content of process heat produced and Bf is the exergy content of fuel input. ge are the Gibbs functions of reactants (shown with r) and products (shown with p) for stoichiometric reaction of fuel evaluated at 1 bar and 298 K.5) The exergy of the process heat produced is given by Bp = ms[(h-hc). he are enthalpies and gi.4) where hi.7) εp = Bp Qp and rph = We Qp (6.3) ⎞ ⎟ ⎟ ⎟ ⎠ (6. Other parameters employed in the Case Study are isentropic efficiencies of compressor and turbine of 70. hence considered all exergy as earlier discussed.Exergy and Environmental Considerations in Gas Turbine Technology and Applications 55 Where We is work. temperature of condensate return is 373 K. Bilgen calculated the composition of the products of combustion of natural gas with 226% air (in moles) as follows: . and in both cases.325 kPa. efficiencies using the above equations as follows.6% respectively. intake air temperature same as ISO condition of 288K. Expressions for the energy and exergy terms above were given by Bilgen as follows: E f = ∑ p ne he − ∑ r ni hi y1 ⎛ yO 2 ⎜ B f = ( ∑ r ni gi − ∑ p ne ge ) + RTo ln ⎜ y x1 y x2 ⎜ CO2 H 2 O ⎝ (6. process steam is saturated at 2026 kPa. yiα is the mole fraction of component I in the environment. Plant capacity factor was assumed to be 80%.8a. A fuel exergy factor is defined as εf = Bf Ef (6. natural gas was used as fuel.6) where ms and s are the mass and entropy of the steam produced. and 60% relative humidity and they are from a case study earlier reported for an industrial gas turbine (the GE LM2500PE reported by Rice (1987) and Huang (1990).1 and 6. The data for Case Study I appear in Table 6.To(s-sc)] (6. Further. both at the process heat pressure. ε.4% and 92.3 were considered in detail. Bilgen (2000): ε= εf η ⎡ rph +ε p ⎤ ⎢ 1+ rph ⎥ ⎣ ⎦ (6. and fuel utilization. 1. 2 HO2. Base-load gas turbine data for Case Study I of Bilgen (2000).3. Table 6. He also presented the following parameters from his study which agreed quite well with those of Rice (1987) and Huang (1990): cycle efficiency. and 6. air flow. exergy efficiency.2. Table 6. 0 NO2. specific work output. Process heat results of Bilgen (2000) appear in Table 6. 0. and power-to-heat ratio compared quite well with Huang (1990). The cycle efficiency of 37. The slow variation of the second law efficiency with power-to-heat ratio indicates that the exergy content of the steam plus power generated from the steam turbine is little degraded. 6.56 Gas Turbines 1 CO2. The exergy efficiency of the cogeneration system is 50. 6. Comparison of the results of Bilgen (2000) with those of Rice (1987) and Huang (1990). 0 CO. 0 NO.001 OH.3 is for the cogeneration system.4 below. yielding a 40% improvement.06% while Bilgen reports an exergy efficiency of only 35.62% in Table 6.2. The trends of the 1st and 2nd law efficiencies in the figure are quite consistent with equations 6.3 below is for the gas turbine without cogeneration while the fuel efficiency of 77.515 N2. 4. 24.78% for the system without cogeneration. This implies a 105% efficiency improvement. Fig. and exhaust temperature compared quite well with Rice (1987) and fuel utilization efficiency.4 below shows the 1st law and exergy (2nd law) efficiency and % steam extraction as a function of power-to-heat ratio.8b.52 O2.02% in the same Table 6. . 4. Fig. . 6.4. shows the 1st law and exergy (2nd law) efficiency and % steam extraction as a function of power-to-heat ratio. Process heat results of Bilgen (2000).Exergy and Environmental Considerations in Gas Turbine Technology and Applications 57 Table 6. Exergy analysis of integrated gasification combined cycle gas turbine (IGCC) plants Integrated Gasification Combined Cycle (IGCC) plants.4. .) as earlier noted in the section on Conventional and New Environmental-conscious Aero and Industrial Gas Turbine Fuels. Total power. lignocellulosic plants. steam turbine power.XXX below. 6. (2007) and shown schematically in Fig. process heat production and payback period as a function of the power-to-heat ratio. Fig. total power. A schematic of a coal-fired gasifier in an integrated coal gasification combined cycle gas turbine plant (ICGCC) plant appears in Fig. The Energy Utilization Diagram (EUD) popularized by the Ishida group and discussed in section 6 of this chapter was used to highlight the exergy losses in the various sub-systems of the plant. We shall consider a biogas-fired integrated gasification steam-injected gas turbine (BIG/STIG) plant studied by Fagbenle et al. 6.5 shows power from the steam turbine. have an integrated fuel production unit (gasifier) which provides the fuel (normally gaseous) required by the gas turbine combustors. The EUD is a useful tool for exergy analysis of chemical processes and plants in which the energy level or availability factor (A) is plotted against the energytransformation quantity (AH). The process steam production (in t/h) follows the same relationship as that of the % steam extraction in Fig. 6.58 Gas Turbines Similarly. as distinct from the general Combined Cycle/Cogeneration plants. enabling easy identification of subsystems with potentials for performance improvement.5. The feed into the gasifier could be a solid hydrocarbon (usually coal) or biomass (e. 6. 6.6 below. agricultural wastes. Fig.g. process heat production and payback period as a function of the power-to-heat ratio. etc. to total entropy change in the system must be greater than or equal to zero. by the 2nd law of thermodynamics. and blast steam required by the gasifier chemical process.2 bar leaves the compressor. the equality being for isentropic (lossless) processes. The adiabatic combustion temperature was found from the 1st Law to be 1895K but a more realistic (from metallurgical standpoint) turbine inlet temperature (TIT) of 1450 K was used in the analysis.e. Also. Air flow of 141 kg/s and at 32.10) By the 1st law of thermodynamics. since the energy released by the energy donor must equal that gained by the energy acceptor. The turbine exhausts at 410 °C (TET) into a Heat Recovery Steam Generator (HRSG) which produces steam for three purposes: injection steam into the turbine for blade cooling.11) ∑ i Δε i = −To ∑ i ΔSi The availability-factor or the energy level (an intensive parameter) is defined by (6.9 kg/s is fed into the combustor while the remaining 9. i.6 consists of a 53 MW gas turbine plant fuelled by fuel gas (syngas assumed to be largely CH4) from a biogas gasifier and gas clean-up system. out of which 131. The BIG/STIG plant of Fig.Exergy and Environmental Considerations in Gas Turbine Technology and Applications 59 Fig. Basis of the Energy Utilization Diagram The exergy change Δεi over all the energy donors and acceptors “i” in the energytransformation system is: ∑ i Δε i = ∑ i (ΔH i − T0 ΔSi ) (6. 6. (2010). The stack gases exhaust into the atmosphere at 151°C.12) . (6. 6. From Emun et al. Simplified diagram of an integrated coal gasification combined cycle (ICGCC) gas turbine plant.XXX. ∑ i ΔSi ≥ 0 Hence. injection steam into the combustor for NOx emission reduction. the first term on the RHS of the above equation is zero.1 kg/s is fed into the gasifier. The exergy loss in the system is thus given by − ∑ Δε i = ∑ i ΔH ea ( Aed − Aea ) ≥ 0 which. This is the EUD diagram and the energy level difference (Aed – Aea) is indicative of the driving force for the energy transformation process.13) It is seen that the relationship between the availability-factor of energy donors and energy acceptors is Aed ≥ Aea since in the energy change of the acceptor process.5 below.6. gives the system exergy loss as: − ∑ Δε i = ∫0 ea ( Aed − Aea )dH ea H (6. . assuming compressor and turbine isentropic efficiencies of 98% each. Δε ΔS A = ΔH = 1 − T0 ΔH (6.60 Gas Turbines Fig. The first law efficiency based on power production alone is 41.5% while it is 45% based on both heat and power.15) A plot of the energy level of the energy donating process (Aed) and the energy accepting process (Aea) against the transformed energy (ΔHea) gives the energy loss in the system as the area between the curves of Aed and Aea. A summary of the operating conditions together with the results of the 1st law efficiencies appears in Table 6. BIG/STIG based on GE LM 5000 aero-derivative gas turbine [Williams (1988)]. in the limit. ΔHea > 0.14) (6. 6. c = 85 + 1.148 0.86.860 . 2nd Law or Exergy Analysis and synthesis Irreversibilities in the turbines and the compressors processes.98)(143) = 2.73 = 86. The processes through the 2 stages each of the turbines (LP & HP) and the compressors (LP & HP) as well as that through the power turbine (PT) are done irreversibly. MW 2.14 .7 MW.278 0.6 MW as detailed below: Gas N2 CO2 CO H2O Exergy loss.5.7 MW c The gross power input to the compressors is therefore Wgross. Irreversibility due to the discharge of hot combustion products at 151°C and 1 bar into the environment is given by Iexh = εstack gases = 3.9 MW For the compressors: 1 Ic = I c = ( η − 1)WLPC & HPC = 1. generated = 140.4 MW.73 = 53.28 0.Exergy and Environmental Considerations in Gas Turbine Technology and Applications 61 Table 6. and their irreversibilities are For the turbines: It = (1 – ηt)WHPT. while the net generated power is Wnet.LPT & PT = (1 – 0. 2 2.8 3.8 2.6.Δεsteam Assuming that the ratio φ of the specific chemical exergy of the fuel to its net calorific value is 0. Icc.8 respectively. HRSG The pinch point on the heat donor side is 546 K and on 512 K on the acceptor side. Net generated power Exhaust temperature Pinch point Minimum ΔT Location Total exergy loss HRSG Combustion chamber Stacks exhaust gases Turbines Compressors Exergy Loss (MW) 76. primarily because the amount of steam injected is relatively small. The largest single subsystem exergy loss occurs in the combustion chamber.6 summarizes the results.9 2. . Table 6.6.17 – 58. between the acceptor and the donor.4 – 7 = 60. Summary of the net generated power and the exegy loss (Irreversibilities) in the BIG/STIG plant.98. % 60.3 Total exergy loss. The cross-hatched area approximately equals the calculated values shown in Table 6. 6.8 6. is given by Icc = εfuel – Δεair . In this case. % 1000 10.98)(5622kJ/kg)(22.7 53.8 MW It is seen that the exergy loss in the combustion chamber (60. The irreversibility of the combustion process can be reduced by reducing the effective temperature difference across which the heat transfer is taking place.1 79. Combustion chamber subsystem reaction The total exergy loss in the combustion chamber. assuming the steam is not dissociated. preheating the reactants with the exhaust stack gases would reduce the irreversibility of the combustion process.8 MW) is about 49% of the fuel exergy (126.7 3.17 MW).7 60.9 1.62 Gas Turbines The Heat Recovery Steam Generator.7 MW. giving ATpinch = 34°C.7 7.1 48. Both the energy and the exergy in the stack gases in this case are both lost.4 MW 151 °C 273 °C 34 °C Fuel exergy.6 2.e.3 1.2 Table 6.Δεsteam = 126. i.9 kg/s) – Δεair .7 and 6. while the irreversibility was found to be IHRSG = 7. The EUD for the HRSG indicates a pinch point of 273°C on the heat donor side and a ΔT = 34°C. being about 79% of the total system exergy loss.3 4. then Icc = (0. The Energy Utilization Diagrams (EUDs) for the combustion chamber and the HRSG The EUD for the combustion chamber and the HRSG appear in Figs. Exergy loss associated with the steam injection mixing process in the combustion chamber has not been taken into consideration. R. 6. Energy-utilization for the combustion chamber. and McConkey. Wikipedia. and Boer. Applied Thermal Engineering 27 (2007) 2220-2225. 34 (2000) 331-338.6. van Nostrand Co. IPIECA Workshop (2004). . Energy-utilization diagram for the heat recovery steam generator (HRSG).. 7. References Emun. (2006). Olakoyejo. Applied Thermodynamics for Engineering Technologists. Layi. O. D.Exergy and Environmental Considerations in Gas Turbine Technology and Applications 63 Fig. Energy Conversion and Management 50 (2009) 3147-3157. London. Eastop. Energy Conversion and Management 51 (2010) 1099-1110. 2008. Gadalla. Shepherd. Introduction to the Gas Turbine.. 2008. (2007). Airline Industry Information.T. 1970. 1949. Woudstra. Pirone. T. E. Typical specifications for Jet A-1 Aircraft Fuels. 2nd. May 3.. D. M. 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R. processing and characterization of newer materials / coatings have been greatly aided by novel approaches to materials / coatings design and synthesis that are based on intelligent and unified understanding of the processing structure properties .1. which enhance temperature capability up to 1250ºC. it is not always possible to achieve both high temperature strength and high temperature corrosion resistance simultaneously because some alloying elements help to improve high temperature corrosion resistance while some may help to improve high temperature strength. and reliability. The availability of materials / coatings with requisite combination of properties largely dictates performance improvements of the gas turbines. development. 2M. Yashwanth2 . This is 1Defence I.S. Engineering College. oxidation and hot corrosion. Further. Increased temperatures lead to increased high temperature corrosion i. The efficiency is directly proportional to operating temperature.based superalloys. smart and possess physical and engineering properties superior to the existing materials / coatings are constantly necessitated for continued technical advances in a variety of fields.3 Design and Development of Smartcoatings for Gas Turbines Metallurgical Research Laboratory Kanchanbagh PO.based superalloy developmental efforts has been directed towards improving the alloy high temperature strength with relatively minor concern being shown to its high temperature corrosion resistance. A section of a typical gas turbine engine is shown in Fig.Gurrappa1 and I. performance. It is to be noted that hot sections of engine are dominated by Ni.V.V.S. marine and industrial gas turbines are manufactured exclusively from Ni . Hyderabad-500 058.based superalloys. Hyderabad-501 510. It is rare that an alloying element leads to enhancement both in high temperature strength and the high temperature corrosion resistance.e. The advanced gas turbine engines need to operate at higher temperatures for obtaining maximum efficiency. The blades in modern aero. The majority of Ni . Nadargul. In modern times. the design. The ever increasing demands in gas turbines for cost savings as well as restrictions concerning emission of pollutants and noise require steady improvement in engine efficiency. High temperature corrosion and in particular hot corrosion (type I and II) is highly detrimental as it causes catastrophic failures if proper materials in association with high performance coatings are not chosen [1-3]. India 1.performance relationships for a wide range of materials / coatings. Advances in processing of Ni-based superalloys have allowed evolution of microstructures from equiaxed structures about three decades ago to directionally solidified (DS) multi-grain and single crystal (SC) components today. Introduction Development of newer materials / coatings that are multifunctional. In the presence of pure sodium sulphate. Significance of nickel based superalloys and titanium based alloys in gas turbine engines further complicated for marine applications by the aggressivity of the environment. Formation of precipitates was further confirmed by EPMA measurements [7]. When sulphide phases are formed in superalloys. thereby reducing the superalloy life considerably. no material was left after exposure of 70 hours to the NaCl containing environment and only corrosion products with high volume of oxide scales was reported [7]. there were no cracks and no spallation of oxide scales was reported for other superalloys.3]. It indicates that NaCl plays a significant role in causing severe corrosion. In case of CM 247LC alloy. 1. Hot corrosion of superalloys Fig. In fact many cracks were developed on the scale and subsequently spallation took place for CM 247 LC superalloy. which are especially effective in destroying the corrosion resistance of . Inconel 718 and CM 247 LC corroded in pure Na2SO4 and NaCl containing environments at 900º C. However. Appreciable corrosion was reported for all the superalloys in the presence of NaCl. Sulphur diffusion and formation of metal sulphides preferentially chromium and nickel sulphides was reported to be the influential factor. Among the superalloys. thereby reducing the loadcarrying capacity and potentially leading to catastrophic failure of components [1.2 shows the hot corrosion behavior of few superalloys like Nimonic-75. CM 247 LC was corroded severely indicating that the superalloy is highly susceptible to hot corrosion. the weight loss was less for all the superalloys [7].66 Gas Turbines Fig. These features are known to drastically reduce the superalloy component life and reliability by consuming the material at an unpredictably rapid rate.based alloys are inferior to cobalt and iron base alloys. Nimonic-105. 2. Thus. The appreciable corrosion attack of CM 247 LC superalloy was clearly evidenced by observing large corrosion affected zone (due to appreciable diffusion of corrosive elements present in the environment). which includes sulphur and sodium from the fuel and various halides contained in seawater. Ni. the high temperature corrosion resistance of superalloys is as important as their high temperature strength in gas turbine engines [4-7]. the alloying elements play a significant role and decide the life of superalloys under hot corrosion conditions [9]. However. As hot corroded superalloys at 900ºC in different environments alloys [7-8]. Similarly. the chemistry of new superalloys were greatly influenced by reducing Cr content and increasing rhenium (Re) content with a view to enhance the temperature capability. This type of attack greatly reduces the high temperature strength properties and thereby affects the efficiency of the system due to failure of components during service conditions [10]. which is a great contrast to the first generation superalloys containing about 10% Cr and no Re. 5th generation superalloys contain osmium and ruthenium in addition to high amount of Re and very low content of Cr. adherent and dense chromia layer. the third and 4th generation superalloys contain only 2 to 4% Cr but instead contain about 6% Re. Therefore. Titanium oxide forms beneath the chromia layer and thereby improves the adherence capability of chromia scale [8]. Rhenium is a unique element which can increase high temperature creep strength considerably. It is generally accepted that the high temperature capability increases with decreasing Cr content. It was also reported that the simple Nimonic-75 alloy is more corrosion resistant over complicated CM 247LC because of the presence of small amount of titanium. it makes the superalloys susceptible to high temperature corrosion [10]. 2. which helps in forming a protective. As a result.Design and Development of Smartcoatings for Gas Turbines 67 Pure Na2SO4 90 % Na2SO4 + 10% NaCl Fig. Thus. It is due to the fact that the . in which extensive penetration of sulphur took place into the superalloys leading to the formation of metal sulphides that in turn led to reduction in their mechanical properties resulting catastrophic failures. as the high vapour pressure of its oxide. Therefore. Failure investigations confirmed that it was due to hot corrosion. Typical failed gas turbine blade due to type I and II hot corrosion .68 Gas Turbines superalloys cannot form corrosion resistant alumina or chromia scale because of high Re content. rhenium is a harmful element for high temperature corrosion resistance of Ni-based superalloys. the need to apply high performance coatings for their protection under high temperature conditions as the gas turbine blades experience high temperature corrosion. it is mandatory to prevent oxidation as well as both types of hot corrosion by using appropriate coating technology [11-13] so as to increase the life of gas turbine engine components to the designed service life. Surface coating technologies As mentioned above. molybdenum and vanadium additions to superalloys are helpful in improving the high temperature strength. there are a number of cases reported in the literature where the gas turbine blades suffered severe corrosion due to which failures took place [1-3]. Therefore. 3. but their presence makes the superalloys highly susceptible to hot corrosion [7]. Particularly. Fig.3. It is known that it is not possible to develop an alloy having both high temperature strength and high temperature corrosion resistance simultaneously since alloying elements often have opposing effects on the two properties.e. A typical failed blade is presented in fig. Its effect is similar to Mo on oxidation i. tungsten. Hence. 3. Though diffusion coatings are well bonded to the substrate they have limited compositional flexibility and their usefulness is strongly dependent on substrate chemistry. nickel aluminide is the resulting species. diffusion and overlay. Further. If a point is reached where the aluminium level in a bond coating falls below the level at which protective alumina scale cannot be formed preferentially. aluminium is made to react at the surface of substrate. slow growth rates and optimum adherence of the alumina scales formed on the coatings during high temperature exposure are of significant for component life. The life of a coating is mainly limited by aluminium depletion occurring upon aluminium consumption as a result of alumina scale growth and repeated spallation and re-healing of the alumina scale during oxidation process. These requirements can be fulfilled only by using coatings with sufficiently high aluminium contents to ensure protective alumina scale formation and re-healing after oxide spallation / reaction with the environment. While overlay coatings are generally MCrAlY coatings where M is Ni or NiCo and essentially comprises a mono-aluminide component contained in a more ductile matrix of a solid solution. Research and development on this type of coatings has led to a variety of compositions with improved scale adherence [13]. For coatings applied over Ni-based superalloys.Design and Development of Smartcoatings for Gas Turbines 69 4. In both the cases. The supply of aluminium for formation of protective alumina scale comes largely from the dispersed mono-aluminide phase during the useful life of such coatings. sodium and sulphur present in the corrosive environment to form corresponding compounds. Types of coatings The present coatings are broadly divided into two types. the oxides of silicon and hafnium are soluble in molten basic sulphate and the basic fluxing dominates in the high temperature hot corrosion region (850-950º C) [13]. The underlying mechanism is that hafnium and silicon that are present in the grain boundaries of alumina scale leach out selectively by readily reacting with chlorine. This type of coatings and surface modification is one of the most widely used for tailoring the surface properties of components. vanadium. faster interaction between the corrosive species present in the environment and the non-protective oxides of other . Overlay coatings are typically well bonded and have a wide compositional flexibility. In diffusion coating application process. The most important improvement in the diffusion coatings has been the incorporation of platinum in aluminide coatings [14-18]. forming a layer of mono-aluminide. This results in dislodging the grains of alumina scale and creates instability of the oxide scale and thereby reducing the life of coatings significantly. This process involves the deposition of platinum by electrochemical method followed by aluminizing at the suitable temperature for the required period. The reaction mechanisms leading to reducing the life of coatings containing silicon or hafnium are given below: HfAl2O3 + Na2SO4 + NaCl HfAl2O3+Na2SO4+NaCl+V2O5 SiAl2O3+Na2SO4 + NaCl SiAl2O3 + Na2SO4 + NaCl + V2O5 = = = = NaAlO2 + HfCl4 + SO3 NaAlVO2 +HfCl4 + SO3 NaAlO2 + Na2SiO3 + SO3 NaAlVO2 + Na2SiO3 + SO3 Diffusion and overlay coatings can provide protection against oxidation and hot corrosion and act as bond coats for zirconia based thermal barrier coating (TBC) systems. It was also reported that traces of silicon as well as hafnium in MCrAlY coatings reduce the coating life drastically [13]. Surface engineering techniques Surface engineering technique. vapour deposition. Therefore. Hardening & cladding f. Diffusion coating processes c. Electro-deposition b. Thermal spray techniques d. the constituents of ceramic thermal barrier coatings react easily with the corrosive species and shorten the coating life significantly. Determination of optimum content of aluminium required in MCrAlY coatings for their hot corrosion resistance constituents of the bond coating occurs and thereby affects the coating life considerably under hot corrosion conditions. 5. It is very clear that aluminium plays a major role in affecting the hot corrosion resistance of MCrAlY alloys though the concentration of other alloying elements remains constant [13]. should not only be effective but also economical. Therefore. Another important aspect is the selection of suitable surface engineering technique by which the coatings are applied since the life of a coating depends not only on coating composition but also on the surface engineering technique employed for its application. diffusion and thermal spraying techniques are widely in use to improve the surface of components for hot corrosion resistance. Selective surface hardening by transformation of phase and g. selection of appropriate surface engineering technique as well as suitable coating composition becomes a challenging task. thermal spray and . The following are the most common surface engineering techniques available at present: a. Ion implantation e. Particularly. 4.70 Gas Turbines 350 WEIGHT LOSS (mg/cm ) 2 300 250 200 150 100 50 0 0 2 4 6 8 10 12 14 % O F ALUM INIU M Fig. Electro-deposition. Fig. Further. optimum content of aluminium in the coatings is extremely necessary to enhance their lifetime.4 illustrates the influence of aluminium on weight loss in the MCrAlY based coating model alloys. which modifies properties of the component’s surface to enhance their performance. Ideally a single coating should satisfy both the requirements. which provides protection and it. chromium rich layer forms chromia scale at a faster rate and provides protection. The intermediate chromium rich phase provides protection under low temperature hot corrosion conditions. Under type II hot corrosion conditions. then aluminium to provide a chemically graded structure. Therefore. enriched first in chromium. hot corrosion is a major problem and in fact decides the life of components. it is possible to obtain total protection for the gas turbine engines under all operating conditions which in turn possible to achieve ever greater efficiency of advanced gas turbine engines. However. Under high temperature oxidation and type I hot corrosion conditions.1 Concepts Gas turbines used in aero engines suffer from high temperature oxidation and hot corrosion when they move across the sea. the development of smart coatings design involves the preparation of multilayered coating consisting of an appropriate MCrAlY base. In marine and industrial gas turbines. offers less protection under low temperature conditions. systematic research in simulating gas turbine engine conditions has been lacking. It helps to improve the durability of TBCs as well since TBC performance is essentially depends on the life of bond coatings [26-29] and hence necessitates compositionally optimised bond coatings. the outer layer of the coating forms alumina scale. This optimum protection is possible because of the formation of most suitable protective oxide scale in each temperature range of operation envisaged. Hot corrosion takes place under two temperature ranges and named type I (800-950ºC) and type II (600-750ºC). while . the smart bond coating should promote slow growth rates of protective scales for enhanced service life. It is possible for a coating only if it contains chromium and aluminium rich graded coatings. Such characteristics are possible with only MCrAlY (where M is Ni or NiCo) type bond coatings. Researchers in the field were attempted to innovate new coating compositions by using different application techniques and concepts [19-25]. Thus. 6. the coating essentially respond to local temperature in such a way that it will form either alumina or chromia protective scale as appropriate. The base coating should be a standard MCrAlY coating enriched with aluminum at its outer surface and a chromium rich layer at its inner surface. High performance coatings should combat high temperature oxidation and both forms of hot corrosion as gas turbines encounter all the problems during service. High purity alumina scales offer best protection against high temperature oxidation and type I hot corrosion and chromia scales against type II hot corrosion. With this type of coatings only. the smart coating can provide optimum protection by responding suitably to the temperatures that are encountered under actual service conditions of gas turbine engines. Smart coatings 6. In this sense. Additionally.Design and Development of Smartcoatings for Gas Turbines 71 vapour deposition techniques are the most efficient techniques for prolonging the life of components significantly. It is pertinent to note that the smart coating should have optimum composition with sufficient reservoir of critical elements like aluminium and chromium to form protective oxide scales depending on the surrounding temperatures. If a single coating can operate successfully over a range of temperatures with different forms of corrosion attack like type I and II hot corrosion and high temperature oxidation. the coating responds to its environment in a pseudo-intelligent manner and hence the name SMART COATING. but a combination of techniques is quite useful. Thus. a smart bond coating has been developed which is optimised compositionally and promotes appropriate protective scale formation depending on the surrounding environmental conditions that enhances the durability of TBC. selection of suitable surface engineering techniques to produce a quality coating is extremely essential. extensive research essentially helps to establish the process parameters of each surface engineering technique.2. the third layer as that of MCrAlY coating composition and the bottom diffusion layer should contain heavy elements.5). Each zone has its specific microstructure with definite composition. Therefore. The first layer should contain high amount of aluminium. As mentioned earlier.3 Performance of a developed smart coating Recently. which in turn the life of CM 247 LC superalloy components. Therefore. diffusion. coating thickness. the order of usage of selected techniques is also important. Diffusion barrier coatings at the bottom help in preventing inter-diffusion of coating and substrate elements. Application of suitable diffusion barrier on the superalloy followed by an optimized MCrAlY coating and chromized treatment to get Cr rich coating and then electroplating followed by pack cementation makes it possible to obtain graded structure as desired. Further.1 Selection of suitable surface engineering technique Preparation of smart coatings is really a challenging task because the performance of coatings basically depends on it. thickness. Alternatively. one has to be extremely careful in selection and utilizing the techniques for production of high performance coatings in order to achieve maximum efficiency. type I and type II hot corrosion [10]. the smart coating permits operation of gas turbine engines over a wide range of temperatures successfully for more than the designed life and helps in enhancing the efficiency significantly by effectively preventing oxidation. The performances of various compositions of MCrAlY bond . The composition of each zone requires detailed analysis to understand the effect of smart coating. The microstructure of each zone varies depending on the coating composition and surface engineering technique used. 6. suitable annealing treatments etc. the smart coating is a graded coating consisting of different zones (Fig. to obtain a smart coating of desired characteristics.72 Gas Turbines aluminium rich surface layer provides resistance to high temperature oxidation and type I hot corrosion. the second layer should be rich with chromium. The selection of technique for coating preparation should be based on the parameters that are controllable to get required microstructure. electro-plating and laser treatments appear to be more effective in producing smart coatings. multiple layers of optimized MCrAlY coatings rich with Cr and Al on diffusion barrier coating followed by pack cementation by using combination of surface engineering techniques makes it possible to obtain smart coatings. However. Among the surface engineering techniques.2 Preparation 6. coating techniques and superior performance of smart coatings over conventional coatings. Here. selection of a single technique may not be of any help. obtaining an appropriate microstructure by identifying suitable surface engineering technique is of paramount importance. 6. The microstructures of coatings also play a significant role in enhancing the life of components. Therefore. thermal spraying. Extensive research both at the laboratory and field augment to establish the appropriate coating compositions. microstructures. Among the coatings. Thick ceramic coatings could not help in improving the hot corrosion resistance of superalloys further due to adherence problem associated with spallation at higher temperatures. which was found to be optimum. It was also observed that the bond coating promoted protective alumina scale formation at 900ºC in the same environments (Fig. Table I presents the life of uncoated superalloy.6).7 & 8). The results indicate that 100 µm thick TBC improved the superalloy life by four hundred fifty times to that of bare superalloy. without TBC and chromia and alumina scale in the presence of TBC at the same environmental conditions and provides maximum life to the TBC which in turn the superalloy components. Slow growth rates and optimum adherence of protective scales forming on .7 & 9). neither sulphur nor oxygen was diffused into the coating indicating an excellent protection provided by 300 µm thick TBC in association with a smart bond coating to the superalloy.9. Under such environmental conditions i. 5.6). the bond coating promoted chromia and alumina scale formation that is clearly observed in Fig. adherent and protective alumina scale on the surface of the bond coating during high temperature corrosion at 900ºC (Fig. It was also evident that 300 µm thick TBC in association with compositionally optimised 125 µm thick NiCoCrAlY bond coating (smart bond coating) enhanced the superalloy life by about 600 times. The high performance of this coating is due to its ability to form continuous. It was observed that yttria and zirconia are still intact even after continuous exposure of 1175 hours and not reacted with the corrosive elements (Figs.e. It is known that TBC reduces the temperature of bond coating / substrate by about 200ºC. the MCrAlY type bond coatings can provide protection against oxidation and hot corrosion and act as bond coatings for zirconia based thermal barrier coating systems.Design and Development of Smartcoatings for Gas Turbines 73 Aluminium rich zone Chromium rich zone Optmised MCrAlY coating Diffusion barrier Fig. As already mentioned. NiCoCrAlY coating exhibited a maximum life of more than 300 hours. Further.e. A schematic representation of microstructure of a smart coating coatings applied on CM 247 LC superalloy (without TBC) were evaluated systematically at 900ºC in simulating gas turbine engine environments. It indicates that the NiCoCrAlY bond coating forms alumina scale at 900ºC i. The maximum life of NiCoCrAlY (smart coating) + 300 µm thick TBC was attributed to the formation of protective alumina and chromia scales not only on the surface of bond coating but also on the TBC surface (Fig. It indicates that the substrate or bond coating temperature is about 700ºC only. smart coating as well as different thicknesses of zirconia based TBCs at 900ºC in simulating gas turbine engine environments. at 700ºC. Life times of CM 247 LC alloy with smart coating + different thicknesses of thermal barrier coatings in 90%Na2SO4 + 5% NaCl + 5% V2O5 environments at 900ºC Na V Al S O W Fig. 6. Elemental distribution of 125 μm thick smart coating after hot corrosion studies .74 Type of coating Uncoated superalloy Smart coating Smart coating +100 µm TBC Smart coating +200 µm TBC Smart coating +300 µm TBC Smart coating +400 µm TBC Life (hours) <2 300 910 975 1175 1170 Gas Turbines Table I. Elemental distribution of 300 μm thick TBC + smart coating (external layer) after hot corrosion studies .Design and Development of Smartcoatings for Gas Turbines 75 BSE Al Cr Na V Y Zr S O Fig. 7. These requirements can be fulfilled only by using compositionally optimised coatings with sufficiently high aluminium and chromium contents to ensure protective scale formation and re-healing after reaction with the environment. Elemental distribution of 300 μm thick TBC + smart coating (internal layer) after hot corrosion studies the bond coatings during high temperature exposure are of significant for component life. If a point is reached where the aluminium and chromium level in the bond coatings falls below the level at which protective scales cannot be formed preferentially. faster interaction between the corrosive species present in the environment by penetrating through the pores of TBC and the non-protective oxides of other constituents of the bond coating occurs and thereby affects the coatings life considerably.76 BSE Al Gas Turbines Cr Na V Y Zr S O Fig. 8. The performance of the smart bond coating was confirmed by employing advanced characterisation techniques. . The lives of coatings are mainly limited by aluminium and chromium depletion occurring upon their consumption as a result of alumina and chromia scale growth and repeated reaction with the corrosive species. the developed bond coating exhibited intelligence behaviour both in the presence and absence of TBC and formed suitable protective scales and hence named as smart bond coating. vanadium. it is a potential bond coating for advanced gas turbines of different types i. The developmental work in this area has successfully resulted a smart coating. aero. Summary The design and development of smart coatings to combat type I & type II hot corrosion and high temperature oxidation in gas turbines is a challenging problem to the Corrosion Engineer. which is essential for advanced gas turbines for their increased efficiency. marine and industrial for their protection against high temperature oxidation. type I and type II hot corrosion. Line scan data of hot corroded two layered smart coating showing alumina and chromia scale formation both on top coating surface as well as at the interface Hence. Therefore.e. 9. Thus. Another important observation is the formation of protective alumina and chromia scales on the surface of TBC as well and prevented the diffusion of corrosive elements like chlorine. a smart bond coating was successfully developed for TBCs that promotes appropriate protective scales preferentially depending on the environmental conditions and enhances the life of superalloy components significantly. 7.Design and Development of Smartcoatings for Gas Turbines 77 O O Cr Cr Al Al Fig. which provided an excellent protection to the superalloys against all the concerns that are . sulphur and oxygen. Kuroda.K. & Tech..Rapp. J.D.J.H. NACE. Solid Struct. Mater.H.J. European Commission. India.Sci. Sci.Lehnert and H..Gogia. Mater..Vialas. N. p 115 [27] M. Surf. Mater.Techonol. A. Sato and H. Sci..A. Forum. Shemesh and R.R. Acta Mater. 19 (2003) 178 [10] I. 3 (1987) 554 [6] R. Sci. Tech. 8. J. Appl.) R. Eng.Stover. Adv.Ali. E. Res. H.A. N. Harada.Windover. and their priority of use in order to prove their performance. Watanabe and H.T. Yamaguchi.Matson. microstructure. A22 (2004) 1208 [22] C.. P.Technol. Ohnuma. Mater.F.Y.Murakami and S. 1 (1972) 171 [19] M.E. 149 (2002) 62 [24] Y.Q-Nusier and G. Kuroda. 24 (2004) 1745 [20] F. Electrodep.Rodriguez and E.R.Gurrappa. Further research is highly essential for their understanding and to develop alternative smart coatings. Mater. & Tech. Stringer. B. Sci.Encinas-Oropesa. Mater. Mater. Houston. Mater.. D.Boettinger. 38 (1997) 137 [9] I.Pieraggi. H. Bangalore. 11 (2004) 589 [2] J. 3 (1987) 726 [7] I.org/jom. Simms. 251-254 (1997) 483 [12] S. A.Radcliff. Katamoda.Gurrappa.W. 9 (2002) 31 [4] J. D.html) [26] I. Kawagishi. Coat.Yashwanth. A. A.Technol.W. A 303 (2001) 100 . Mater.Technol.Murakami and S. W. D. Sci.. Texas. A.Gogia. Coat.78 Gas Turbines being experienced by all types of gas turbines. D. 9..Gurrappa and A. Intl.. thickness. Final Project Report. G. JOM (2008) 31 (www.. Platinum Met..Mater.K.Rev. J.Kerkhof and D.Campbell.. Met.M. 197 (2001) 199 [29] R. Extensive research is needed both at the laboratory level and field to optimize coating composition.Newaz. H.. Vac. Surf.Gurrappa. G. 22 (2007) 206 [25] K.Coat. H. Surf. J.Lee. Tech. M. Technol.MacClanahan. Shariat.. (Submitted) [14] I... I.Kuroda.Stekovic.S.N. Treat..M.Gurrappa. J. J..Eng. Acknowledgements The authors are grateful to the Defence Research and Development Organisation for providing financial assistance. H.Bacos. Intl.Sci. 38 (2001) 3329 [28] D. Engineering Failure Analysis.S. High Temperature Corrosion (ed.Ericsson and S. Grunling.Sci.High Temp. Sci. August 2004.Kawakita. (1981) p 519 [18] G. Tech. 50 (2002) 775 [23] L. J.Singer. Khajavi and M. 45 (2001) 124 [15] I.. ‘Design and Development of smart Coatings for Aerospace applications’. U. Wear.P. Durable Surf. Suzuki and H.Gurrappa. Rev. Engineering Failure Analysis. Herrera.R. Oxid. 50 (1999) 353 [8] I. 17 (2001) 581 [16] I.Chiang. Kuppusami. Harada. identification of appropriate surface engineering techniques. F.Kattner. Poquillon. July 2008 [11] H.S. Josso.Gurrappa. Eliaz. T. S.G.Meier. Latanision.R. Singheiser. 3 (1987) 482 [5] A. Sci. M. Murakami.Gurrappa. Murakami and T.Gurrappa.Evans..M. Wu. Mumm and A.Vassen. 252 (2002) 264 [3] N. Proceedings of International convention on Surface Engineering (INCOSURF 2004)..Pettit and G.Nicholls. Surf.Meinhardt. Gallardo. 168 (2003) 62-69 [21] P.Audino.V.Thermal. 9 (2008) 33002 [13] I.Monceau.tms. Mater.Wu. 139 (2001) 216 [17] K. References [1] M. Rechtanbacher and L. Favorski2 1Boreskov 2Central Institute of Catalysis. Introduction Gas turbine power plants (GTPPs) of low power (tens of kW to 1. 1992. This technology makes it possible to decrease significantly the temperature in the combustion zone relative to traditional GTPP combustion chambers with separate supply of fuel and air to the combustion zone. Zakharov2. Parmon et al. Boris I. .. Vladimir M. Parmon1. The main approach used today to decrease the emission of nitrogen oxides from GTPPs is based on the use of the so-called homogeneous combustion chambers working with premixed lean fuel-air mixtures with two-fold excess of air. Pfefferle & Pfeferle. 1983.4 Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants Zinfer R. Dalla Betta & RostrupNielsen. which. solves heat supply and water shortage problems. In the last decade. may negatively affect combustion stability. that it results in low heat release rates. 1995. Ismagilov et al. Valentin N. the concentration of nitrogen oxides in the flue gases decreases from 100 ppm to 1020 ppm. Zagoruiko1. efficient combustion of homogeneous fuel-air mixture is achieved at larger excess of air and much lower temperatures in the zone of chemical reactions compared to modern homogeneous combustion chambers. 1995. Nadezhda V. Mikhail A. The most efficient way to decrease emissions of nitrogen oxides in GTPPs is to use catalytic combustion of fuel (Trimm.. in turn. The decrease of NOx formation is principally the result of the low flame temperatures that are encountered under lean conditions (Correa 1992). This is 1.. 2010). Ismagilov1. In the catalytic chamber. Kerzhentsev1. the obvious advantages of the catalytic combustion chambers in GTPPs initiated intense scientific and applied studies in the USA (Catalytica) and Japan (Kawasaki Heavy Industries) which are aimed at development of such chambers for GTPPs for various applications (Dalla Betta et al. The application of gas turbine technologies saves fuel. 1987. Yashnik1. The downside of this approach is. Dalla Betta & Tsurumi. The nominal efficiency of GTTPs belonging to different generations varies from 24% to 38% (average weighted efficiency – 29%). The main GTPP drawback is significant emission of toxic nitrogen oxides due to high temperature combustion of the gas fuel. Ismagilov & Kerzhentsev.5 times higher than that of combined heat power plants. Andrei N. As a result. Moscow Russia 1. 1999.. Novosibirsk Institute of Aviation Motors. 1999.5-2 MW) are promising autonomous sources of energy and heat. 630090. Ismagilov et al. Svetlana A. 2002).. Ismagilov & Kerzhentsev 1990. however. Braynin2 and Oleg N. Shikina1. Dalla Betta & Velasco. 1995. Such catalyst has to possess high mechanical strength and the ability to initiate methane oxidation in lean mixtures at low temperatures 620-720 K and maintain stable oxidation during long time at temperatures above 1200 K (Dalla Betta et al. 1999). 2002). T out > 900 °C) (Carroni et al. 1999).80 Gas Turbines The catalyst in a gas-turbine combustor has to withstand continuous operation for at least 10. Dalla Betta & Rostrup-Nielsen. 2. which would provide minimum emissions of NOx. CO and HC at moderate temperatures (930-950°C). 2000. Therefore. intended for decentralized power supply. the improvement of the catalyst stability is an urgent problem. Use of palladium as the active component in the high-temperature oxidation of methane is most promising.000 h under severe operation conditions: high gas hourly space velocity (GHSV) and temperatures over 1200 K (McCarty et al.. It results in the catalyst destruction. It is well known that catalysts based on noble metals are most active in oxidation reactions. Material development is therefore one of the key issues in the development of catalytic combustion for gas turbines. which is the least readily oxidizable hydrocarbon. 1999). It is very difficult to find catalysts meeting requirements of both high activity at low temperature and good thermal stability at high temperatures. application of such catalysts requires many problems to be solved. McCarty et al. Carroni et al. it is necessary to produce catalysts capable of initiating methane oxidation at minimum possible temperatures and withstanding long-term exposure to temperatures above 930°C. 1995. peeling of the support and loss of noble metals decreasing the catalytic activity and shortening the catalyst lifetime. So. 1986).. which consists largely of methane. especially in the presence of water vapor. Today catalysts for gas turbines are prepared in the form of monoliths from foil made of special corrosion-resistant alloys with deposited porous support and the active component based on platinum and/or palladium (Dalla Betta et al. They can initiate combustion at low temperatures. The main problems are related to the high temperature of gas typical for modern gas turbines that requires the catalyst to operate at temperatures exceeding 1200 K for prolonged periods of time (total operation time of modern GTPPs reaches 100000 hours) (McCarty et al. 1995) and a relatively low volatility in comparison with other noble metals. in catalytic gas combustors generally staged combustion is employed: a highly reactive catalyst for the lowtemperature (350 °C < Tin < 450 °C) conversion of CH4 must be combined with a second catalyst which converts fuel at higher temperatures (Tin approx. This is because palladium has a high specific activity in this reaction (Burch & Hayes.. but it is inappropriate to use them above 750°C because of a high volatility of the noble metals (Arai et al. as was . Therefore. However. 700 °C. In this chapter we present our results on development and study of alternative granular catalysts with reduced Pd content for methane catalytic combustion in mini gas turbines of 400-500 kW power with regenerative cycle. 1995. Selection of catalysts for application in gas turbine combustors The most available fuel for GTPPs is natural gas. Lee & Trimm. The small power of these turbines results in reduced catalyst loading and makes possible the use of granular catalysts which are less expensive and can be easily manufactured using existing industrial facilities. The use of metal supports at temperatures above 900°C is limited due to possible thermal corrosion. 1995a.. One of the approaches to solve this problem is based on development of catalysts on granulated supports and design of a catalytic package for GTPP combustion chamber. 2003). Tsikoza et al. The specific surface area of hexaaluminates and. La. 1996.. 1992). Alternative catalytic systems for methane combustion are catalysts based on hexaaluminates and transition metal oxides. 2003. Tsikoza et al. irrespective of their specific surface area. Ismagilov et al. it was shown that introducing 0. 1999). Yue et al. It is these properties of palladium that attract researchers' interest to its behavior in the methane oxidation reaction. so a decrease in temperature leads to the reoxidation of Pd to PdOx in air.. 2002.Mg)LaAl11O19 resulted in a significant increase in the catalyst activity expressed as a 110°C decrease in the temperature of 50% methane conversion (T50%). raises the activity and thermal stability of the catalyst through an increase in the degree of dispersion of the active component and in its aggregation stability (Baldwin & Burch. palladium exists as PdOx which undergoes reduction to palladium metal as the temperature is further raised.. the temperature dependence of the methane conversion always shows a hysteresis (Farrauto et al. Su et al.. a synergistic effect in the Pd–(Mn. Fe. Machida et al. This yields Mn–Al–O compounds of complex composition (solid solutions and/or hexaaluminates) at 1300°C. Ni) (Machida et al. 1998a.. 900°C. it was found that Mn–Al–O catalysts supported on γ-Al2O3 containing χ-Al2O3 and modified with Mg. It is well known that. 1999). 1995. Co. We believe that the high degree of disorder of the χ-Al2O3 structure in comparison with γ-Al2O3 favors deeper interaction of manganese and modifiers with the support at the impregnation and low-temperature calcination stages.. The activity of these catalysts in hydrocarbon oxidation can be enhanced by their calcination at 900–1100°C..or α-Al2O3 or Al2O3 modified with rare-earth metal oxides.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 81 determined by studying the interaction of the metals with oxygen at 730–1730°C (McCarty et al. Supporting of palladium on a substrate. 2003. In our earlier work (Yashnik et al. the hexaaluminates are much less active than the palladium catalysts.. 2006). Pd with oxygen chemisorbed on its surface. 2002). 1990. In our works (Tsikoza et al. Groppi et al. and this is why they are very stable up to high temperatures. 1999. two types of catalysts were selected for further development and study: (1) active Pd catalysts with low ignition temperature for initiation of methane combustion and (2) thermally stable hexaaluminate catalysts for methane combustion at temperatures over 900°C. 1998. such as La and Ba. There is still no consensus as to what form of oxidized palladium — bulk PdO. their activity in methane oxidation depend on the preparation method (Chouldhary et al. Su et al. up to 800° C. In addition. As a consequence.. This reaction is reversible up to ca. Thus. Lyubovsky & Pfefferle.. . Lyubovsky & Pfefferle. 1989).5 wt % Pd into the hexaaluminate (Mn. primarily γ.. 2002. Liotta & Deganello. accordingly. where A is a rare-earth or alkaline-earth metal. 2003). due to which the catalysts are stable and highly active in methane oxidation. Burch. It was demonstrated earlier that thermally stable catalysts could be prepared from manganese oxides (Tsikoza et al. and B is a transition metal with an atomic radius comparable to the radius of aluminum (B = Mn. Hexaaluminates are the class of compounds with a general formula ABxAl12-xO19 . In view of this. 2003. 1998 b. based on literature data and our research results... Hexaaluminates form from oxides at temperatures above 1200°C. or Pd particles covered by PdO —is the most active species in combustion ((McCarty.Mg)LaA11O19 system was detected. Ozawa et al. 2005). However. 1987.. Cr. 2003).. there have been attempts to enhance the catalytic activity of hexaaluminates by introducing Pd (Jang et al. 1999). or Ce were more active and thermally more stable (up to 1300°C) than the same catalysts supported on pure γ-Al2O3.. 5 2.65 wt % Pd. Before being loaded with palladium. The catalyst calcination temperature was 900°C. the samples were dried and calcined at 400°C. mm Bulk density. g/cm3 Pore volume (H2O). Mn-La–Al2O3. .7 0. It contained 11 wt % manganese oxides in terms of MnO2. mm Inner diameter.. This allowed us to increase the specific surface area of the sample. Pd–Mn–La–Al2O3. Koryabkina et al.5 0. for this reason.. It was similar in composition to the commercial catalyst IKT-12-40.5 7.45 180 270 γ-Al2O3 Ring-shaped Al2O3 7. The pilot batch of the catalyst was designated IK-12-62-2. This catalyst was prepared on the ring-shaped support by successive incipient-wetness impregnation with lanthanum and manganese nitrate solutions. It was prepared by the incipient-wetness impregnation of the support with a cerium nitrate (Ce(NO3)3 . These concentrations of manganese and lanthanum are sufficient to ensure a high catalytic activity and stability of the catalyst (Yashnik et al. Thereafter. mm Length.82 Gas Turbines 3. its pilot batch is hereafter designated IKT-12-40A. Mn–Al2O3. 2006). This catalyst was prepared on the ring-shaped support by successive incipient-wetness impregnation of alumina with lanthanum and manganese nitrate solutions using the procedure described in (Yashnik et al. m2/g Crushing strength under static conditions. 6H2O) solution and then with an aqueous Pd(NO3)2 solution. kg/cm2 Phase composition Spherical Al2O3 2. Koryabkina et al.1 Preparation of catalysts In catalyst preparation. After supporting of palladium. it was additionally calcined at 1000°C. The resulting catalyst contained 8–11 wt % Mn in terms of MnO2.. Synthesis of granular catalysts for methane combustion 3. Ismagilov et al.. the samples were loaded with a palladium nitrate solution by impregnation. Property Diameter. The catalyst was prepared on the ring-shaped support and contained 12 wt %CeO2 and 2 wt % Pd. Their characteristics are presented in Table 1.45 200 23 60% γ-Al2O3 40% χ-Al2O3 Table 1. The calcination temperature was 1000°C. 2006). 1991. It contained 8–11 wt % manganese in terms of MnO2 and 10–12 wt % lanthanum in terms of La2O3. 10–12 wt % La in terms of La2O3.8 0. and was 0. 2006) and was equal to the onset temperature of hexaaluminate phase formation. Final calcination was carried out at 1000°C. cm3/g Specific surface area. 1991.. lower than the temperature used in our previous study (Yashnik et al.. The pilot catalyst batch was designated IK-12-60-2.The catalyst was prepared on the ring-shaped support by the incipient wetness impregnation of the support with an aqueous manganese nitrate (Mn(NO3)2* 6H2O) solution. Physicochemical properties of the spherical and ring-shaped aluminas Pd–Ce–Al2O3. we used γ-alumina supports developed at the Boreskov Institute of Catalysis (Shepeleva et al. 1996) prepared in the form of spheres and rings. Next.. 1991.2–2. the alumina support modified with cerium was calcined at 600°C.5 0. The pilot catalyst batch was designated IK-12-61. The catalyst IK-12-61 modified with 0. The Mn catalysts are more tolerant to high temperatures and are less prone to aggregation than the Pd–Ce catalyst. Over the first 50 h of testing. we investigated how their physicochemical and catalytic properties depend on their chemical composition. The results of these tests are presented in Table 3.. the NOx concentration in the reaction products remained at the 0–1 ppm level. the specific surface area and pore volume of the IK-12-60-2 catalyst decreased because of the coarsening of alumina particles and the onset of α-Al2O3 formation via the δAl2O3 – α-Al2O3 phase transition under prolonged heating.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 83 3. 1). The degree of dispersion of metallic Pd0 decreased with testing time. Tsikoza et al. The active component PdO underwent partial decomposition to Pd0. and hexaaluminate phase) contents. namely. and the active component introduction method (Yashnik et al. The ignition temperature and the methane–air combustion efficiency remained unchanged at least over 100 h of testing. In the next 50 h. The catalysts on the ring-shaped alumina support (IK-12-60-2..65 wt % palladium (IK. the initial activity of the catalyst IK-12-61 did not decrease. IK-1262-2) were tested in natural gas combustion at 930°C in the pilot plant at the Boreskov Institute of Catalysis. and the reaction products were almost free of CO and NOx. Service life tests suggested that all catalysts are tolerant to high temperatures (up to 930°C) and to the action of the reaction medium. . 2006. the active component and modifier (manganese. However. and T50 increased by 50°C. the chemical nature of Mn and Pd precursors. Tsikoza et al. which is known to be resistant to high temperatures. lanthanum.2 Characterization of catalysts When developing and optimizing the catalysts based on manganese oxides. including those additionally containing lanthanum and palladium.. IKT-12-40A. Measuring the catalytic activity of catalyst samples in methane oxidation allowed us to find the optimal catalytic systems. α-Al2O3 and a (Mn. Tign falls from 365 to 350°C. The investigation of the physicochemical properties of the initial samples (Table 2) showed that. 2002. the textural parameters stabilized and the degree of dispersion of the remaining PdO phase increased. but even gradually increased during testing: in 200 h. Al)Al2O4 solid solution in IKT-12-40A and manganese hexaaluminate in IK-12-61 and IK-12-62-2. Some changes in the phase composition of the catalysts occur because of the formation of high-temperature phases. The activity of the catalysts Pd–Ce–Al2O3 and MnOx–Al2O3 decreased slightly. The catalytic activity of the hexaaluminate-based samples in the CH4 oxidation reaction after 100-h-long testing was similar to the activity of the fresh catalysts: T50 is 470–480°C for the catalyst IK-12-61 and 363–380°C for IK-12-62-2 at GHSV = 1000 h–1 (Fig. whose properties are listed in Table 2. the active component PdO is finely dispersed and this allows one to initiate combustion of the methane–air mixture at low temperatures. The catalyst IK-12-60-2 retained its high activity over 100 h: the ignition temperature (Tign) was 240°C. palladium. the calcination temperature. The manganese-containing catalysts were less active: with these catalysts. 2003). IK-12-61. The initial catalysts based on Mn and La oxides (IK-12-61 and IK-12-62-2) contain the hexaaluminate phase. in IK-12-60-2. The durability tests altered the structural and textural characteristics of the catalysts (Table 4). and the CO concentration decreased from 55 to 34 ppm. Tign and the residual CO and NOx contents were higher than with IK-12-60-2.12-62-2) allowed us to reduce the ignition temperature of the methane–air mixture almost by 100°C and the CO concentration in the reaction products by more than one order of magnitude. The activity of the catalysts Pd–Ce–Al2O3 and MnOx–Al2O3 decreased slightly. °C wt % Gas Turbines Catalyst Phase composition* VΣ Strength.4 (~400 A.1 S33=1100).γ-Al2O3 Mn – 7. γ-Al2O3# is a solid solution based on γ-Al2O3. LaAlO3.84 CalciChemical nation compotempesition.9 Al2O3.937 A). Mn2O3 MnLaAl11O19 (S37 Mn – 6.**** °C IK-12-60-2 1000 δ-Al2O3.units) in diffraction patterns. arb. ** Ssp is specific surface area.PdO La – 9. 50% CH4.0 mm at GHSV = 1000 h-1 and methane concentration in air equal to 1%. Table 2.1 (a = 7.5-1. α-Al2O3. γLa – 10. h 100 100 200 200 Tign . ppm CO 0-1 84-55 55-34 2-3 NOx 0-1 0-1 0-1 0-1 Catalyst IK-12-60-2 IKT-12-40A IK-12-61 IK-12-62-2 Test duration.9 = 60). CeO2 (~200 Å. Ssp.1 (~180 and 250 Å. 1). rature.1 Al2O3# MnLaAl11O19 (S37 Pd – 0. S39 = 480) Mixture of (δ + γ)Mn – 6. ****T. Results of catalyst durability tests in natural gas combustion at 930°C in a bench testing unit at the Boreskov Institute of Catalysis The catalytic activity of the hexaaluminate-based samples in the CH4 oxidation reaction after 100-h-long testing was similar to the activity of the fresh catalysts: T50 is 470–480°C for the catalyst IK-12-61 and 363–380°C for IK-12-62-2 at GHSV = 1000 h–1 (Fig. m2/g kg/cm2 cm3/g T. S39 = 70) 74 0. . °C 240 350 365-350 290 Table 3.23 23 400 1000 43 0.18 34 420 IK-12-62-2 1000 48 - 25 385 *The particle size was derived from the size of coherent-scattering domain region. 50% CH4 is temperature of 50% methane conversion on catalyst fraction 0.** (Nads)***. Relative phase contents were estimated from peak areas (Si. Pd – 2. ***VΣ (Nads) is pore volume found form N2 adsorption.65 – traces). PdO Ce – 10.26 24 330 IKT-1240A IK-12-61 900 80 0. and T50 increased by 50°C. Physicochemical and catalytic properties of the initial catalysts on spherical and ring-shaped supports Residual content. 17 19 IKT-12-40A 100 66 0. PdO (~ 300 Å. α-Al2O3 MnLaAl11O19 (S37 = 250). α-Al2O3 MnLaAl11O19 (S37 = 240). PdO (>400 Ǻ. cm3/g Strength. α-Al2O3 (traces). α-Al2O3 (traces). Physicochemical properties of the catalysts after durability tests in natural gas combustion . Pdo (S41 = 90). S39 = 160) MnLaAl11O19 (S37 = 230). LaAlO3.18 0. S39 = 180). Pdo (>400 Ǻ. S47 = 40). PdO (400 Ǻ. Al)Al2O4 (a = 8.15 0.151 Ǻ) MnLaAl11O19 (S37 = 240). S33 = 1100). PdO (~ 160 Å. γ-Al2O3# (a = 7. m2/g VΣ (Nads). S39 = 180). α-Al2O3 MnLaAl11O19 (S37 = 230). S47 = 120) δ-Al2O3.18 21 100 38 0. CeO2 (~200 Å. α-Al2O3 (S29 = 30). γ-Al2O3# (a = 7. γ-Al2O3# (а = 7.13 30 28 28 IK-12-62-2 50 31 - 29 100 30 - 32 200 30 - 35 Table 4. Pdº (~500 Å. S39 = 160) MnLaAl11O19 (S37 = 340). Pdº (~ 300 Å. CeO2 (~200 Å. S39 = 180). Pdo (>400 Ǻ.937 Ǻ).937 Ǻ). LaAlO3. PdO (>400 Ǻ. kg/cm2 42 0.937 Ǻ). LaAlO3. S33 = 1100). γ-Al2O3-based solid solution (Mn. S47 = 40) Ssp.22 19 IK-12-61 30 50 100 41 33 31 0.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 85 Catalyst IK-12-60-2 Test duration. S47 = 80) α-Al2O3. h 50 Phase composition δ-Al2O3. after 100 h testing. % 40 20 0 200 300 400 500 600 700 o Temperature.5–1. 2. GHSV=1000 h– 1) on the catalysts: IK-12-61: ▲ – initial. ◆ .after 100 h testing in CH4 combustion at 930°C. ◊. The volume of the catalytic package was 1. IK-12-62-2: △.after 50 h. Catalyst IK-12-60-2 IKT-12-40A IK-12-61 IK-12-62-2 k0.initial.86 Gas Turbines 100 80 60 X. and 48000 h–1. we used activity data for the 0. Experimental studies of natural gas combustion in a catalytic combustion chamber 5. C Fig.0 mm size fractions of the catalysts in methane oxidation at GHSV = 1000. s–1 4. The results obtained by data processing in the plug flow approximation are presented in Table 5.29 × 107 105 105 E. 4. The reaction order with respect to methane was found to be equal to 1.3 L.2 71. Kinetic parameters of the total methane oxidation reaction 5.36 × 1. ●-after 30 h.09 × 105 Table 5.09 × 3.8 1. 24000. Temperature dependences of methane conversion (1 vol % CH4 in air. Kinetic studies of methane catalytic oxidation Kinetic studies of methane catalytic oxidation were performed in a flow reactor. The obtained kinetic parameters were used further for modeling of methane combustion.1 Experimental procedures Experimental studies of natural gas combustion were carried out in a stainless-steel tubular vertical catalytic combustion chamber (CCC) with an internal diameter of 80 mm. □. kJ/mol 81. .after 50 h.2 63. ■ . In kinetic calculations.4 71. The CCC is schematically shown in Fig. 1. 4–6.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 87 Fig. Natural gas was introduced into the combustion chamber after reaching the light-off temperature. The air/fuel equivalence ratio (α) was selected to be close to the minimum value of this parameter in the operating regime of full-power GTPP (α= 6. When the desired temperature regime was reached. the temperature at the chamber exit (Tex) was 900–985°C.8). the temperature in the catalyst bed increased and reached the values close to the desired ones in 30–40 min. . Due to the natural gas combustion. The gas probes were also analyzed in parallel using ECOM-AC gas analyzer. temperatures along the length of the catalytic chamber were measured. The gas phase composition at the CCC outlet was analyzed using a “Kristall2000 M” gas chromatograph.000 h−1. Schematic view of the catalytic combustion chamber: T-1 to T-4: thermocouples. the GHSV of the fuel–air mixture was 8500–15. The temperature mode was corrected by smooth variation of the air and natural gas flows. sampling 1–5: gas samplers. The inlet temperature of the fuel–air mixture (Tin) was varied between 470 and 600°C. The radial temperature profile was measured before and after the pilot-plant tests. A reference manometer was used to measure the pressures in the catalyst bed. 2. and it initiates methane combustion. Mn–La–Al2O3 and Pd–Mn– La–Al2O3 catalysts shaped as rings were tested for 72–120 h in a temperature cycle mode. two high temperature catalysts with different granule shape. Mn–Al2O3.10%) of the highly active Pd-Ce-catalyst is located in the upstream section at low temperature. In this case. 3. The highly active Pd-catalyst in the upstream section initiates methane oxidation. the high temperature resistant catalyst in the larger middle section provides stable methane combustion.2 Tests of the catalytic combustion chamber with uniform catalyst package First. This combination with a short bed of spherical catalyst provides rather high methane combustion efficiency at a minor increase of pressure drop. two ring shaped catalysts with different catalytic activity. uniform loading with ring shaped high temperature resistant oxide catalyst 2.. 2009. Therefore.88 Gas Turbines The catalytic packages studied are schematically presented in Fig. Schemes of uniform (1) and structured (2–4) loading of the reactor and photo of granulated catalyst (Yashnik et al. 4. 1. 2010) 5. the methane conversion should increase with change of granule shape as: ring < cylinder < sphere. three catalysts with different catalytic activity and fractional void volume. According to the results of modeling. 3. Fig.. The bicomponent spherical Pd-Mn-Al-O catalyst with a low Pd-content and low fractional void volume in the downstream section improves the efficiency regarding the residual traces. However. we tested CCC loaded with one catalyst. a short bed (ca. . Such experiments allowed us to analyze the perspectives of using manganese–alumina catalysts and evaluate their catalytic properties in natural gas combustion by such parameters as outlet temperature and emission of hydrocarbons. the use of spherical catalyst for entire reactor is impossible due to a high pressure drop. Such loading will be hereafter denoted as “uniform” and provides for one-stage combustion of the natural gas–air mixture. the reactor consists of two sections: the first with ring shaped oxide catalyst (or Pd-Mn-Al-O) and the second downstream section with spherical catalyst having lower fractional void volume. The larger bed of high temperature resistant oxide catalyst in the downstream section provides high efficiency of methane combustion. This design of catalytic reactor allows a reduction of total Pd loading and an increase of methane combustion efficiency at a low inlet temperature. 3. Ismagilov et al. (2) Mn–La–Al2O3 (Tin – 600 °C). The dynamics of changes in the activity of different catalysts are presented in Fig. operation time in CCC at GHSV: 14. respectively. 4.24 s (GHSV = 15. Methane conversion vs. The combustion process was carried out at GHSV= 15. These data indicate that the mass transfer of the reagents and reaction products to/from the catalyst surface substantially affects the total CCC efficiency in methane combustion at the inlet temperature 600 ◦C. i. In both cases the CCC efficiency also depended on contact time. (3) Pd–Mn–La–Al2O3 (Tin – 575–580 °C). At this temperature methane .900–15. The contact time increase from 0. The value of α was maintained at 6. Table 6 compares the outlet temperatures and emissions of CH4 and CO during natural gas combustion over Mn–Al2O3 catalysts with different fractional compositions at GHSV= 8500– 15.6% to 97.7–6. The data presented in Fig. 4.9.100 h−1 and α = 6.8. lower fractional void volume of the catalyst bed. the activity of the Mn– Al2O3 catalyst gradually decreased as evidenced by gradual increase of the methane and CO concentration at the CCC outlet.000 h−1. 4. Even at a low load on the catalyst (GHSV = 8500 h−1) the methane conversion was 97% whereas the methane and CO emissions at the outlet were 500 and 300 ppm. Note that under similar CCC operation conditions the application of catalyst granules with the external diameter 7.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 89 The temperature cycle mode consisted of four cycles of gas combustion. The methane conversion decreased from 99.9% during the first 50–54 h on stream.000 h−1) to 0.5 mm allowed for a 10-fold decrease of the methane emission and 30-fold decrease of the CO emission. Mn–La–Al2O3 and Pd– Mn–La–Al2O3 differ both by their activity and stability. Fig. catalyst cooling and repeated start of the combustion process.5 mm).42 s (GHSV = 8500 h−1) affected more significantly the efficiency of CCC loaded with the catalyst with smaller internal and external diameters of the granules (7.8–6. Then the catalyst activity stabilized and did not change in the following 80 h on stream (Fig. curve 1). The height of the catalytic package was 300 mm.e. respectively (Table 6).000 h−1 and inlet temperature 580–600 ◦C.It was shown that the methane combustion efficiency over large catalyst granules with the external ring diameter 15mm was low. At the end of the experiment the methane and CO concentrations stabilized at 330 and 110 ppm. Uniform catalyst package loaded with: (1) Mn–Al2O3 (Tin – 600 °C). 4 indicate that the catalysts Mn–Al2O3. For example. Т3 – 195 mm. the obtained results demonstrate that the activity of the Pd–Mn–La–Al2O3 catalyst was higher than that of the catalysts without Pd.89 98.5 7.. These data agree with the work (Hayashi et al. ppm 102 41 9 943 616 344 СNOx ppm 1 2 1 1 2 2 XCH4 % 97.10 5. 2006.87 96. Tsikoza et al. 4).1 309 243 180 324 267 204 GHSV. However.7% to 99. Table 6.13 α 6.69 93. 1995).41 6. It was shown that modification of Mn-alumina catalysts with oxides of rare earth metals allowed a considerable increase of thermal stability of the catalysts due to the . tion. pressure and the catalyst channel density.78 6. GGN is volume flow rate of natural gas.. 4. respectively. 2002. the activity decrease was less dramatic compared to the Mn–Al2O3 catalyst (Fig.90 Gair is volume flow rate of air. m3/h l/h mm 7. Note that the Pd–Mn–La–Al2O3 catalyst showed these values of the residual CH4 and CO concentrations at a lower inlet temperature 575 °C than the Mn–La– Al2O3 catalyst that showed similar values at 600 °C inlet temperature. which is confirmed by substantial improvement of methane conversion with the increase of the catalysts geometrical surface. Tsikoza et al.70 6. CCH4. XCH4 is methane conversion. especially at temperature 700 °C the homogeneous oxidation reaction was prevailing. Т4 – 280 mm.5 7. These results of the catalysts testing under the above conditions are in good agreement with our results on the study of the catalysts activity in methane oxidation in a laboratory reactor (Yashnik et al.67 6.5% to 99. curve 3). CCO.2 15.0 11. CO and NOx.. h-1 14900 11500 8500 14800 11500 8500 Tin °С 577 567 571 590 570 562 T1* °С 659 677 728 623 604 591 T2* °С 867 903 923 763 783 790 T3* °С 920 926 925 898 909 903 Т4* °С 917 905 896 918 919 897 ССH4. The concentrations of methane and CO stabilized at 100 and 85 ppm. *temperatures measured by thermocouples placed along the catalyst bed at different distances from the CCC inlet: Т1 – 25 mm.4% (Fig. 1995) where the authors showed the dependences of relative contributions of heterogeneous and homogeneous methane oxidation reactions on the monolithic Pt–Pd catalyst on the inlet temperature.. curve 2) and from 99. Parameters of methane combustion over Mn-Al2O3 catalysts with different fractional composition The activity of Mn–La–Al2O3 and Pd–Mn–La–Al2O3 catalysts also decreased in the first 30– 40 h on stream.1 19. Thus. GNG. The methane conversion over Mn–La–Al2O3 and Pd–Mn–La–Al2O3 catalysts decreased from 99. ppm 328 164 48 987 630 504 СCO. FracGair. 2003). CNOx are outlet concentrations of CH4.28 97. 4. The NOx concentration at the outlet of the catalyst package did not exceed 0–2 ppm on all the catalysts.90 Gas Turbines oxidation proceeds mainly on the catalyst surface and the contribution of homogeneous reactions is negligible.0 11. Т2 – 110 mm.68 99. Meanwhile.. at the same time in the monolith with larger channels (100 cpsi).4 15. correspondingly. Placing the catalysts with small cells (200 cpsi) in the front part of the reactor allowed the increase of heat release there at 600 °C (Hayashi et al. the stability of this catalyst was comparable to that of Mn–La–Al2O3 being determined by the Mn– hexaaluminate phase. The stability of these catalysts was much higher than that of the catalyst based on Mn oxide.3% (Fig.5 15 15 15 19.. alternative methods of increasing the methane conversion are required.3% to 99. If the surface reaction in the channel with a catalyst takes place in the diffusion-controlled regime.900.2 and 7. Fig.000 h−1. 5. 1989) suggested feeding the fuel–air mixture to a monolith catalyst consisting of alternating channels with an active component and without it. 1993) and Westinghouse Electric Corp.5 wt. Tin = 600 °C. 5 shows that methane conversion above 99. American companies Catalytica (Dalla Betta & Tsurumi. one of the ways to increase the CCC efficiency is to use multistage (multizone) combustion. However.% Pd into Mn–La–Al2O3 resulted in a substantial decrease of the lightoff temperature of the air–natural gas mixture (Yashnik et al. As it is known from the literature. Fig.. Introduction of 0. 2006.2 showed that its decrease (enrichment of the fuel–air mixture with methane) resulted in a growth of the temperature at the outlet of the catalyst bed and. So high temperature is undesirable because the catalyst overheating during prolonged operation will inevitably lead to its deactivation. The fuel–air mixture exiting the inert channels is burnt at the exit of the monolith catalyst. Dependence of methane conversion (filled symbols) and catalyst temperature at the CCC outlet (open symbols) during methane combustion in CCC loaded with Mn–La–Al2O3 catalyst on α.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 91 formation of manganese–hexaaluminate phase (Yashnik et al.9% was observed when the temperature in the catalyst bed exceeded 980°C. 23 and 14 mbar at GHSV= 14. Mn–La–Al2O3 and Pd–Mn–La–Al2O3 was 35. For instance.5 mm × 7. GHSV= 15. 2006).500 and 8500 h−1.. Several methods for stepwise combustion of hydrocarbon fuels in the GTPP CCC have been implemented. adiabatic heating to the flame temperature does not occur because the heat is transferred to the inert channel of the monolith.5 mm rings for the catalysts Mn–Al2O3. The variation of α between 6. Tsikoza et al. increase of the methane conversion.93% and the temperature grew from 937 to 992 ◦C at GHSV= 15. respectively. (Young & Carl. These values are less 4% of the total pressure which was 1 bar.000 h−1. Figure 5 shows the effect of the air/fuel equivalence ratio on the outlet temperature and methane conversion over the catalyst package loaded with the Mn–La–Al2O3 catalyst. .5 mm × 2. consequently.. 2002). The pressure drop on the full height of the catalyst bed for uniform loading of the catalysts in the form of 7. when α was decreased from 7 to 6.2. Therefore. This method allows one to control the temperature profile by varying the catalyst activity in different zones of the catalytic combustion chamber. the methane conversion increased from 99. 11. and Pd–Mn–La–Al2O3. Methane conversion vs. transition metal oxides). Using the Pd–Mn–La–Al2O3 catalyst as an example we studied the effect of the catalyst bed fractional void volume on the methane conversion in CCC.8).5 mm rings having the fractional void volume (ε) 0. The catalytic activity is regulated by varying the concentration of the noble metal (most often Pd) in the range of 5–20 wt. The maximum CO concentration is observed in this region. spheres (Tin – 575–580◦C.9).7–6. One can see that more than 90% of methane is oxidized at the distance ca. Further combustion of methane and CO to concentrations below 10 ppm is observed mostly at 280–340 mm from the inlet of Fig.% or the nature of the active component (noble metal.5 mm × 7.%. (3) combined catalyst package: Mn–La–Al2O3. 1993. Fig. 5.42 was placed near the outlet of the package. It was also suggested (Dalla Betta & Velasco.8).5 mm × 2. 1997) it was suggested to use multi-section catalysts with different levels of activity to carry out combustion in the kinetically controlled regime.1. GHSV= 12.3 Tests of CCC with combined two-stage catalyst package We suggested a design of a two-stage catalyst package consisting of catalysts with the same chemical composition but different fractional compositions. 6) and decrease the methane concentration from 85 ppm to 0–5mm and the CO concentration to 4–8 ppm at inlet temperature 580°C and α in the range of 6. 7 presents the methane and CO profiles along the reactor length. Pfefferle.500 h−1. rings and spheres (Tin = 575–580 ◦C.92 Gas Turbines In patents (Dalla Betta & Tsurumi.8–6. A catalyst with low ignition temperature requiring minimal heating is placed at the entrance zone whereas a catalyst resistant to the action of high temperatures is placed at the exit.7–6. The application of the spherical catalyst at the CCC outlet made it possible to achieve over 99.7–7.500 h−1. 200 mm from the inlet.52.6 wt. α= 6. 6.9% combustion efficiency (Fig. rings. The main part of the catalyst package was loaded with the catalyst formed as 7. (2) combined catalyst package: Pd–Mn–La–Al2O3. GHSV= 12. α = 6. operation time in CCC for different catalyst packages: (1) uniform catalyst package Pd–Mn–La–Al2O3. A catalyst layer with 60 mm height consisting of 4–5 mm spherical granules with fractional void volume 0. α = 6. GHSV= 15. The total Pd concentration in the catalyst package was 0. rings (Tin = 575–580 ◦C. 100 h−1. 2002) to use a two-stage monolithic catalyst combined from catalytic systems with different thermal stabilities. . The total Pd content in CCC was much lower . The layer of this catalyst has a higher density and higher geometrical area. 6. which provides more efficient use of the catalyst. curve 2) where the total Pd content was 0. The ratio of the layer heights was similar to that used in the previous test – 280/60mm. The methane conversion over the catalyst package Pd–Mn–La–Al2O3 (rings)/Pd–Mn–La–Al2O3 (spheres) decreased from 99. 7. The pressure drop in the two-stage catalyst package was 48 mbar at GHSV= 12. We carried out tests on a combined catalyst package consisting on Mn–La–Al2O3 (rings) and Pd–Mn–La– Al2O3 (spheres) and compared the methane conversion with the results of the previous test. the substitution of the more active catalyst with a less active and a 6-fold decrease of the total Pd content (Fig. i. we determined the role of catalyst activity in the total CCC efficiency. However. increase of the efficiency of the use of the catalyst granules even at a relatively short length of the CCC results in a noticeable improvement of the overall CCC efficiency at a low total Pd loading. The methane conversion over the catalyst package Mn–La–Al2O3 (rings)/Pd–Mn–La–Al2O3 (spheres) at the inlet temperature . The tests of CCC with a combined two-stage catalyst package at lower inlet temperature showed that the inlet temperature decrease from 580 to 470 ◦C decreased the methane combustion efficiency. 6.% because most of the catalyst package consisted of the Mn–La–Al2O3 catalyst. such CCC design produced a larger pressure drop than the uniform catalyst package with ring-shaped catalysts.7% with methane and CO concentrations increasing to 37 and 150 ppm. respectively.%. and thus increases the CCC efficiency. in the area where the spherical catalyst is loaded. Profiles of methane and CO concentrations along the reactor length during combustion of natural gas on a combined catalyst package Pd–Mn–La–Al2O3: 280 mm of rings and 60 mm of spherical granules (Tin = 580 ◦C. The pressure drop in the layer of the spherical Pd–Mn–La–Al2O3 catalyst was 20 and 13 mbar. However.000 h−1.93% to 99.500 h−1 and 30 mbar at GHSV= 10.6 wt.e.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 93 Fig. curve 3) did not decrease the methane combustion efficiency compared to the previous test (Fig. Then. GHSV= 12.1 wt. Thus.500 h−1). respectively. the catalyst package.about 0. The activity of this catalyst (T50% CH4) is lower than that of Pd–Mn–La–Al2O3 (Table 3). Finally. The tests were carried out at the inlet temperature 470 ◦C.5 mm rings. the ratio of the heights of ring and spherical granules was 280/60mm. the use of the three-stage combined catalyst package including a thin layer of the active palladium–ceria catalyst located at the CCC entrance before the main oxide catalyst bed allows us to increase the CCC efficiency for methane combustion and obtain required low methane emission value of 10 ppm at low inlet temperature 470◦C. This additional catalyst layer provides the initial methane conversion and temperature increase before the main catalyst bed.2. The methane concentration profile shows a sharp concentration fall in the inlet zone where the Pd–Ce–Al2O3 catalyst is located. respectively. The main decrease of the concentration from 1.5 mm × 7. we used a model of a steady-state adiabatic plug-flow reactor.4 Tests of CCC with combined three-stage catalyst package In the three-stage catalyst package we placed a highly active Pd–Ce–Al2O3 catalyst with 2 wt. Then.94 Gas Turbines 470 ◦C was only 99. The concentration of the CO intermediate initially grows.000 h−1 and α = 5. temperature. Pd–Mn–La–Al2O3 catalyst in the form of 4–5 mm spherical granules was placed in the downstream part of the catalyst package. Most of the package consisted of Mn–La–Al2O3 catalyst.4% with methane and CO concentrations 90 and 220 ppm. Both catalysts were shaped as 7. 8b. In the inlet zone filled with the Pd–Ce–Al2O3 catalyst at 25 mm from the inlet the feed is heated from 470 to 580 ◦C due to catalytic combustion of methane. Similarly to the tests of two-stage packages. Thus. The calculation of the temperature profiles and methane conversion was performed at variation of catalyst methane oxidation activity and geometry of catalyst granules. 6. Under such conditions the temperature at the outlet zone of the catalyst package remained at about 950 ◦C. the CO concentration also decreases from 300 to 40 ppm in the Mn–La–Al2O3 bed. 3.4% to 170 ppm takes place in the zone of the main catalyst Mn–La–Al2O3 (40–280 mm). Then at the CCC exit in the layer of the spherical Pd–Mn–La–Al2O3 catalyst the residual amounts of methane burn from 170 to 0–10 ppm concentrations. Modeling of methane combustion processes in a catalytic combustor 6. . The increase of the methane combustion efficiency at low inlet temperature was made possible by organizing a three-stage catalyst package. The ratio of the catalyst layer heights was 40/240/60mm. ratio of bed lengths of different catalysts in the package. when most methane is oxidized. The pressure drop in the catalyst package was 29–30 mbar. The profiles of the methane and CO concentrations along the CCC length are shown in Fig.5 mm × 2. The latter temperature is sufficiently high for effective functioning of the main Mn–La–Al2O3 catalyst bed. For calculation of the catalyst package performance. pressure and gas space velocity in the combustor. 5.1 Model description The catalytic packages used in modeling are schematically presented in Fig. GHSV= 10.% Pd at the entrance zone. Further temperature growth from 580 to 950◦C takes place on this catalyst. residual CO is burned in the spherical Pd–Mn–La–Al2O3 catalyst to 10 ppm concentrations. Figure 8a shows the temperature profile along the CCC length. P is the operating pressure (bar). The reaction rate was calculated using Eqs. E is the activation energy (J mol-1). 8. η is efficiency factor (dimensionless). Р0 is the pressure (bar) at which the reaction kinetics is studied experimentally (in this case it is equal to 1 bar).Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 95 Fig. ε is the fractional void volume in the catalyst bed (dimensionless). α = 5. ССН4 is the methane concentration (molar fraction).2). R is the univeral gas constant (J mol-1K-1). . k0 is the pre-exponential factor of the kinetic constant (s-1).000 h−1. GHSV= 10. Profiles of temperature (a) and methane and CO concentrations (b) along the reactor length during combustion of natural gas on a combined catalyst package Pd–Mn–La– Al2O3/Mn–La–Al2O3/Pd–Ce–Al2O3 (Tin = 470 ◦C. (1) and (2): ⎛ P⎞ W = k CCH 4 ⎜ ⎟ ⎜P ⎟ ⎝ 0⎠ (1) ⎛ E/R ⎞ k = η k0 (1 − ε )exp ⎜ − ⎟ T ⎠ ⎝ (2) where k is the kinetic constant (s-1). ΔTAD is the adiabatic heating of the reaction (K). was determined using the standard Thiele equation for the first-order reaction (Malinovskaya et al. A heat and mass steady-state model of an ideal displacement adiabatic reactor was used in the simulations of the catalyst bed: u ∂CCH 4 ∂ * = −W = β (CCH 4 − CCH 4 ) (3) u ∂TG α in = xCCH 4 ΔTAD = (TC − TG ) ∂ cp (4) = 0 ⇒ C i = C iin . Modeling of the process was performed taking into account the influence of the internal and external diffusion on the kinetic parameters (k0 and E) for the reaction CH4 + 2O2 →CO2 + 2H2O proceeding on each individual catalyst.%. C* and C are methane concentrations at the surface of the catalyst grain and in the gas flow. 1979) with representation of different catalyst pellets shapes by the spheres of equivalent diameter. accounting for the internal mass transfer limitations. the effects of the catalyst granule shape and size on characteristics of the process of catalytic methane combustion: methane conversion. index in corresponds to the conditions at the reactor inlet. 2007): methane concentration in methane– air mixture 1.2 Selection of shape and size of catalyst granules The ultra-low emission characteristics of catalytic combustion chamber are determined not only by the catalyst activity but also by geometric parameters of the catalyst package.96 Gas Turbines The values of kinetic parameters (k0 and E) determined earlier in kinetic experiments over these catalysts (Ismagilov et al. α is the heat exchange coefficient (Wm−3 K−1). The efficiency factor η. temperature in the bed and pressure drop were studied. and hence on the residual methane content and the temperature in the catalyst bed. The methane combustion modeling shows that the shape of the catalyst granules has a substantial effect on methane conversion. This effect increases with a decrease of the inlet temperature and an increase of the space velocity. TG and TC are gas and catalyst temperatures (K). being most marked for catalysts with . Equations used for calculations are presented in detail elsewhere (Ismagilov et al. GHSV = 5000–40.. 6. 2008) (see Table 5) were used in the calculations.. which are responsible for the efficiency of mass and heat transfer in the fixed catalyst bed. T = Tin (5) Here u is the superficial linear gas flow velocity in the reactor reduced to standard conditions and full reactor cross-section area (m/s). correspondingly. cp is the gas thermal capacity (Jm−3 K−1). Ismagilov et al. x is the methane conversion..5 vol. ℓ is the coordinate along the reactor height (m).000 h-1 and inlet temperature 723–873 K. Therefore. The calculations were performed for typical operation conditions of the CCC (Parmon et al. 2010). 2008. The model CCC was represented by a tubular reactor with 80 mm inner diameter and 300 mm catalyst bed height. respectively. 1975). such as the bed height and the shape and size of catalyst granules. β is the mass exchange coefficient for methane (s−1). The mass and heat transfer coefficients were calculated according to the equations presented in (Aerov et al. and 4. and cylindrical granules with size 7.%. respectively.0 mm. 9 shows simulated profiles of the residual methane content upon methane oxidation in uniform beds of the IK-12-61 catalysts with different shape: ring Fig. α = 6.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 97 lower activity. . 823 K (Curve 3) and 873 K (Curve 4) for uniform catalyst package loaded with Mn-La-Al2O3 catalyst (IK-12-61) as ring. 773 K (Curve 2). GHSV at temperatures: 723 K (Curve 1).5 vol.5 mm. Simulated profiles of residual methane concentration (A) and inlet pressures (B) vs.5 mm x 2. Fig.5 mm x 5 mm. spherical.9. 9. Experimental data are presented for comparison: 773 K () and 873 K (Ο). Methane concentration is 1. The CCC diameter is 80 mm and the height is 300 mm. 5.5 mm x 7. At higher GHSV. At 723 K and 10. and the second downstream section with the spherical catalyst having lower fractional void volume. but also to the minimization of the pressure drop in the catalyst bed.2 bar. However.000 h-1 the residual methane content less than 10 ppm is observed at the inlet temperature of 823 K for the beds of both ring-shaped and spherical granules.000 h-1 and a temperature as low as 773 K. the former provides the residual methane concentration 10 times lower than the latter. the use of cylindrical and spherical catalyst for the entire reactor is impossible due to a high pressure drop (Fig. when 20% of the ring-shaped Mn-La-Al2O3 catalyst was replaced by the spherical granules (Figs. 9B. 9B). cylinder (4. . Thus. According to modeling. but neither of the catalyst shapes provides the required methane emission level (not exceeding 10 ppm) at GHSV higher than 5000 h-1. while at 35. For example.0 mm).000 h-1. This combination with a shorter bed of spherical catalyst (about 20%) provides rather high methane combustion efficiency at a minor increase of pressure drop (not exceeding 20%) in comparison with the uniform catalytic package.0 mm) and sphere (5.5 mm × 2.5 and 1. methane content being below 10 ppm at 25.%). at 40. the residual methane contents attained in the beds of spherical and ringshaped granules of IK-12-61 catalyst are different by a factor of 4. Further.000 h-1. This catalytic package has also high efficiency at 40. the residual CH4 content decreased twice and the pressure drop increased only by 18%.3. 10B) is more effective than the one with Mn-La-Al2O3 (Fig.5 mm × 5.5 mm × 7. The catalytic packages with both Pd-Mn-La-Al2O3 and Mn-LaAl2O3 have a similar thermal stability at temperatures up to 1373 K. At similar conditions. at GHSV below 20. in the loading of the CCC with granulated catalysts.3 Variation of the structure of combined catalyst loading in the CCC 6. three types of catalyst packages complying with the above requirements are examined. the methane conversion increases with the change of granule shape in the sequence: ring < cylinder < sphere. 10A). The structured combined catalytic package containing two or three catalysts with optimal catalytic properties and geometrical parameters seems to be promising to meet these two requirements. The simulation of methane combustion process shows that the catalytic package with PdMn-La-Al2O3 (Fig. catalytic packages with a height of 300 mm containing ring-shaped and spherical granules give the pressure loss of up to 0.5 mm). which can result in the reduction of the catalyst lifetime. although at a higher inlet temperature (873 K).5. For instance. the attention should be paid not only to the ultra-low emission characteristics. first of all. It should be noted that at high inlet temperatures and high methane concentrations the maximum temperature in the catalyst bed can be as high as 1373–1473 K.1 Two high temperature catalysts with different granule shapes The reactor consists of two sections: the first one with the ring shaped oxide catalyst Mn-LaAl2O3 or this catalyst modified by Pd (0. the required methane residual concentration is attained only at the increase of the inlet temperature with a similar effect of the granule shape. 9A and 10A).000 h-1 and 873 K.8 wt. 6.5–0. because the CCC having a low light-off temperature of lean methane–air mixtures and high thermal stability provides stable combustion of methane–air mixtures and low emission characteristics.000 h-1 this methane concentration is attained only on the spherical granules and at a higher temperature of 873 K.98 Gas Turbines (7. respectively. As shown in Fig. the light-off temperature and the operation temperature limit of the catalysts should be taken into account. In design of a combined catalytic package with a high efficiency and a long lifetime. 823 K (Curve 3) and 873 K (Curve 4) for combined catalyst package loaded with Mn-La-Al2O3 (A) and Pd-Mn-La-Al2O3 (B) catalysts in accordance with Scheme 2 {ring (7.3.3.2 Two ring shaped catalysts with different catalytic activity In this case. at the same conditions of 40. 6. The larger bed of high temperature tolerant MnLa-Al2O3 or Pd-Mn-La-Al2O3 catalyst in the downstream section provides practically total methane combustion. GHSV at temperatures: 723 K (Curve 1). 773 K (Curve 2). L = 60 mm}. The effect of the variation of the length of the two sections and space velocity on the process parameters was also studied and showed that the optimal loading of highly active Pd catalyst is close to 10% of the total catalyst loading of the CCC. the simulated residual methane content achieved over the former package does not exceed 10 ppm.5 mm x 2. Experimental data are presented for comparison: 743 K () and 853 K (Ο).9. α = 6. however the catalyst package formed from Pd-Mn-La-Al2O3 is also rather efficient. Simulated profiles of residual methane concentration vs. Methane concentration is 1. a short ignition bed (ca. 10. the high temperature tolerant catalyst in the larger middle section provides stable methane .0 mm). Modeling of methane combustion process shows that the use of Pd-CeO2-Al2O3 catalyst is more preferable.%. For example.5 mm x 7. 10%) of the highly active Pd catalyst is located in the upstream section with a lower temperature. while with the latter it is as high as 125 ppm. 6.5 mm). 11).5 vol.000 h-1 and 873 K.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 99 Fig. This design of the catalyst package allows a reduction of the total Pd loading and an increase of methane combustion efficiency at low inlet temperatures.3 Three catalysts with different catalytic activity and fractional void volume The highly active Pd catalyst in the upstream section initiates methane oxidation. The location of a more active catalyst in the upstream section is more advantageous in comparison with a variant of its downstream location (Fig. L = 280 mm} + {sphere (5. 5 vol. L = 260 mm} + Mn-La-Al2O3 {ring 7. 773 K (Curve 2). α = 6.5 mm x 7.5 mm x 2.5 mm x 2. (C) PdCeO2-Al2O3 {ring 7. 9). The bicomponent Pd-Mn-La-Al2O3 catalyst with a low Pd content and low fractional void volume in the downstream section improves the efficiency by removal of methane residual traces.4 Comparison of simulated and experimental data Experimental runs with a model reactor (1.5 mm x 7.5 mm. L = 40 mm}. Simulated profiles of residual methane concentration vs. It should be noted that the cost of the combined catalyst package is not significantly higher than that of the uniform Mn-LaAl2O3 catalyst bed. 823 K (Curve 3) and 873 K (Curve 4) for combined catalyst packages in accordance with Scheme 3 (A and B) and Scheme 4 (C). (B) Pd-Mn-La-Al2O3 {ring 7.5 mm x 2.5 mm. Experimental data are presented for comparison: 743 K () and 853 K (Ο).5 mm x 2.5 mm x 7. 9A. The catalytic package with the spherical or ring-shaped granules of the IC-12-61 catalyst provided methane combustion to 1 ppm and 15 ppm residual methane concentration. L = 40 mm} + Mn-La-Al2O3 {ring 7. (A) Mn-La-Al2O3 {ring 7.%. 10B and 11C). GHSV at temperatures: 723 K (Curve 1). combustion. .0 mm. L = 40 mm}.9. in the pilot test installation at 15.000 h-1 and 773 K and to 2 ppm at 24.3 l catalyst) demonstrated very good correlation with the results of the modeling (Figs. For example.5 mm x 7. 6. The modeling showed that the substitution of 10% of Mn-La-Al2O3 catalyst (Fig. Methane concentration is 1. L = 260 mm} + Pd-Mn-La-Al2O3 {ring 7.100 Gas Turbines Fig.5 mm x 2. For the package operation at a higher GHSV (30.5 mm.5 mm. L = 60 mm}. 11.5 mm x 2.5 mm. an increase of the inlet temperature to 773 K is required.5 mm x 7.5 mm x 7. L = 240 mm} + Pd-Mn-La-Al2O3 {sphere 5.5 mm. 10A) for Pd-CeO2-Al2O3 in the upstream section and the introduction of spherical Pd-Mn-La-Al2O3 catalyst in the downstream section of the catalytic package (Fig. at 20. respectively.000 h-1 the inlet temperature can be reduced from 873 to 723 K. 11C) allow a decrease of the inlet temperature and an increase of GHSV.000 h-1).000 h-1 and 873 K (Fig. 5 mm and 5 mm.000 h-1 and α = 6. Curve 2).5 mm x 7. 2000. 2005). The excess of the experimental values over the simulated ones can be caused by the heat loss. 12. The symbols are experimental data. It is well known that the increase of the surface and the reduction of the void fraction lead to an increase of free radical decay. On the other hand.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 101 Fig.. respectively).000 h-1 as a function of the inlet temperature. Noticeable amount of CO (10–14 ppm. Curve 1) and spheres ( . . respectively. Lower experimental values of the residual methane content in comparison with the calculated ones for the catalyst Pd-Mn-LaAl2O3 in the range of the inlet temperatures 773–823 K are probably due to the contribution of other heterogeneous reactions (different from deep oxidation) and gas-phase homogeneous methane oxidation. Deutschmann et al. 2008). Uniform catalyst package loaded with Mn-LaAl2O3 catalyst (IK-12-61) as rings ( ... respectively) and the void fraction in the catalyst bed (ε = 0..5 mm x 2.8. Carbon monoxide can be formed as an intermediate product of homogeneous methane oxidation.5 mm x 2. The observed deviation of the experimental data on residual methane content from the simulated curves can be explained by two causes.5 mm x 7. Our assumption about the contribution of gas phase methane oxidation agrees with a decrease of the CO concentration when the ring-shaped granules are totally (Fig. Residual methane concentration (A) and CO concentration (B) vs.5 mm x 7.. having size 7. there is strong evidence that the catalyst surface affects the gas-phase chemistry (Sidwell et al. The carbon dioxide reforming and the partial methane oxidation as well as gas phase reactions have not been incorporated into our simulation yet. 2003. which has been shown in the study of methane oxidation in lean mixtures at 900– 1400 K (Reinke et al. 13B) for spherical granules.5 mm and 5 mm. Curve 3) with size 7. The ring-shaped and spherical granules are different by the specific external surface (593 and 693 m-1. inlet temperature of CCC at GHSV = 24. respectively. Chou et al. because we have not observed CO and H2 formation in the kinetic experiments (Ismagilov et al. and Pd-Mn-La-Al2O3 catalyst (IK-12-62-2) as rings ( .5 mm. 2000.42. 12B) was observed in the pilot test installation when the CCC was loaded by ring-shaped and/or spherical catalyst granules with a size 7. Fig.5 and 0.5 mm x 2. Figure 12 shows the correlation between the simulated and experimental data for the residual methane concentrations in a uniform catalytic package with the ring-shaped MnLa-Al2O3 and Pd-Mn-La-Al2O3 catalysts at 24. Aghalayam et al. the lines are calculated data. 12B) or partially substituted (Fig.. The authors made this assumption from comparison of the experimental data with numerical models that include both surface and gas phase chemistry.9. Quiceno et al.. α = 6. 2003) for the oxidation of lean methane–air mixtures. The combustor has a preheating chamber to heat the catalyst to ignition temperature by hot combustion gases and an annular catalyst module with a catalyst loading of 70 kg. 2003).78-7.102 Gas Turbines 2003. CO 4-6 ppm. Testing of the prototype combustor demonstrated high efficiency of methane combustion (>99. 280 mm)/Pd-Mn-La-Al2O3 (sphere. (B) Scheme 2: PdMn-La-Al2O3 (ring. Conclusion Granular catalysts for natural gas combustion in gas turbine power plants were developed: Pd-Ce-Al2O3 catalyst for initiation of methane combustion at low temperatures and the catalysts based on oxides of Mn. GHSV = 15. Fig. 2000). The hexaaluminate catalyst surface is assumed to act as a sink for methyl radicals..000 h-1. α = 6. 2000. 7. GHSV = 15. Quiceno et al. suppressing gas-phase reactions (Sidwell et al. 340 mm) at Tin = 575°C.. Development and testing of a prototype catalytic combustor Based on the research results a prototype catalytic combustor for a gas turbine with a power 400 kW was designed and fabricated at CIAM (Perets et al. It should be noted that nitrogen oxides appeared at all and at low concentrations only if a part of fuel was burned in the preheater.. α = 6.000 h-1. GHSV = 27000-31200 h-1. 2000) and Aghalayam (Aghalayam et al. Profiles of methane ( ) and CO ( ) concentrations and temperatures along the CCC length during combustion of natural gas in a combined catalyst package: (A) Scheme 1: PdMn-La-Al2O3 (ring.97%) and low emission of toxic compounds: NOx 0-5 ppm. outlet temperature 1145-1160 K. 2000).. 14). We also observed that the CO concentration changes along the catalyst bed increasing with the temperature increase up to 1173 K but decreasing at the further rise of the temperature (Fig. 8. HC 6-20 ppm at inlet temperature 835-880 K. 2009) (Fig. (Chou et al. Chou et al. 60 mm) at Tin = 580°C. 13.8.13. The arched profile of the formed CO can be evidence that CO is the intermediate in the multi-step surface reactions mechanism proposed by Deutschmann and coworkers (Deutschmann et al... 13). pressure 5 atm (Table 7). hexaaluminates of Mn and La for high temperature . 0 ppm 0 ppm -1 Regime 2 Modified combustor 840 K 5.13 835-860 K 1145-1160 K 18-20 ppm 4.0 atm 830 g/s (2310 nm3/h) 0 g/s (0 nm3/h) 6.5 nm3/h) 31200 h 6.45 g/s (37.78 880 K 1145 K 6 ppm 4.0 atm 960 g/s (2670 nm3/h) 0. 14.2-6.2 ppm 4. Results of tests of the prototype catalytic combustor methane combustion.6 ppm -1 Table 7. .5 nm3/h) 7.89 g/s (4.9 g/s (37. Scheme and photo of the prototype gas turbine catalytic combustor Characteristic Temperature at the combustor inlet Pressure at the combustor inlet Air flow velocity at the combustor inlet Methane flow velocity in the preheating chamber Methane flow velocity in the combustor GHSV Air/fuel equivalence ratio Temperature at the catalyst bed inlet Temperature at the catalyst bed outlet Concentrations at HC the combustor CO outlet NOx Regime 1 Initial test 880 K 5.5 nm3/h) 27000 h 7. The catalysts based on manganese–hexaaluminate showed high efficiency and thermal stability during combustion of natural gas for more than 200 h at the temperature in the catalyst bed as high as 1223-1258 K.Development of Granular Catalysts and Natural Gas Combustion Technology for Small Gas Turbine Power Plants 103 Catalyst module Preheating chamber Exhaust Methane Methane Fig. The catalytic combustion of natural gas over uniform and combined loadings of granulated manganese-oxide and palladium-containing catalysts was studied for optimization of the design of a catalytic package for use in CCC. The use of 4-5 mm spherical granules in the combined loading increased the pressure drop to 48 mbar at GHSV= 12. T. HC < 10 ppm. Experimental runs in the pilot reactor (1. Fernandes.. Catal. J. T. 0166-9834 . 337-358. The Mn-La-Al2O3 and Pd-Mn-LaAl2O3 catalysts with hexaaluminate structure exhibiting good high-temperature activity and high thermal stability can be recommended for the stable methane combustion at a high combustion efficiency in the CCC downstream section. 265-279.12. 66.6003 10. (1986). Todes..000 h−1.3 kg catalyst) demonstrated very good correlation with the results of the modeling. & Burch. Catalytic combustion of methane over supported palladium catalysts Appl.. 9.. 23-38. Based on the research results a prototype catalytic combustor for a gas turbine with a power 400 kW was designed and fabricated. 1990. RFBR (Grants 06-08-00981 and 07-08-12272) and State Contract 02. (1979). Mhadeshwar. At the catalyst package height 300 mm and GHSV= 8.. Y.. Apparaty so statsionarnym zernistym sloem: Gidravlicheskie i teplovye osnovy raboty (Fixed-Bed Apparatuses: Hydraulic and Thermal Principles of Their Operation).4 and 19. K. & Seiyama. shapes and sizes of pellets has been performed. The highly active Pd-Ce-Al2O3 and Pd-Mn-La-Al2O3 catalysts should be used in the CCC upstream section for the initiation of methane oxidation. vol. Papavassiliou. Yamada. A C1 mechanism for methane oxidation on platinum. & Vlachos. 0021-9517 Arai. Appl. 0166-9834 Baldwin. M. R. Modeling of methane combustion in several types of catalyst packages composed of 1. . H. A26.5mm×2. (1990). The replacement of 20% of the ringshaped Mn-La-Al2O3 catalyst by the spherical low-percentage Pd-hexaaluminate catalyst in the exit part of the CCC downstream section results in improvement of methane combustion efficiency at a minor increase of the pressure drop (not exceeding 20%). N. Catalytic Combustion of Methane over Various Perovskyte-Type Catalysts. M..526. T. However.G.5mm were shown to be the optimal form of the catalysts..5%) is acceptable for afterburning residual unburned fuel and CO at the CCC exit. pp.000 h−1 the pressure drop in the catalyst package was lower than 40 mbar. & Narinskii. Acknowledgments This study was supported by Integration projects of RAS Presidium 7.000 h-1).. CO < 10 ppm. the use of a thin layer of such granules (less than 17. The addition of 10% of the highly active Pd-CeO2-Al2O3 and Pd-Mn-La-Al2O3 catalysts with ring shape in the CCC upstream section of such catalytic package provides the required emission characteristics (CH < 10 ppm) at the low inlet temperature (about 723 K) and the high GHSV of lean methane–air mixtures (>20. A. (2003). 2 or 3 beds of granulated catalysts with different chemical compositions. V.5mm×7. Khimiya. K. Experimental runs with a prototype combustor demonstrated high efficiency of methane combustion (>99.500 h−1 and 30 mbar at GHSV= 10. Catal. 213. B. D. O. This is less than 4% of the total pressure in CCC (1 bar).4.104 Gas Turbines Different schemes of catalytic packages were designed.R. Equchi. Catal.97%) and low emission of toxic compounds: NOx < 1 ppm.E. P. Park. Moscow Aghalayam.500– 15. 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S. 5 Electricity Cogeneration using an Open Gas Turbine University of Maribor (Faculty of Chemistry and Chemical engineering) Slovenia 1. 1. which operate under high pressures.1). Gas turbine 2. combustion chamber fuel air working fluid (outlet gas) high T. Processes. The outlet gas serves as a working fluid (Fig. Important Our main purpose is to use existing gases during chemical processes. Gas turbines operate on the principle that fuel and air will burn in a combustion chamber. p Anita Kovac Kralj turbine −Δ p el. in order to drive a turbine. 2). The high operating pressure at a reactor’s outlet can be exploited to produce electricity using the open gas turbine system (Fig. followed the cleaning at low pressures. Introduction A gas turbine is a rotary engine that extracts energy from a flow of combustion gas. can be exploited for electricity cogeneration. generator Fig. . 2.110 reactor inlet working fuid high T. Air and fuel pass through a compressor into a combustion chamber. An open gas turbine system includes the following process units. Open gas turbine system 3. p Gas Turbines compressor +Δ p turbine −Δ p separator heat exchanger el. Then. 3): • reactor (R) • gas turbine (T) with electric generator • heat exchanger (H) • separator (S). which drives an electric generator. a gas turbine operates by internal combustion. where the liquid product separates off and • compressor (C). Usually. The reactor acts as the combustion chamber of the gas turbine plant. . Our main purpose is to use existing gases from within the chemical processes to drive the turbine by using an open gas turbine system. coupled to an electricity generator. in order (Fig. A conventional power plant uses fuel energy to produce work. Many chemicals are produced under high pressure and at high temperatures. The combustion products are then expanded in a turbine. Open gas turbine system The gas turbine has rendered increasing service within the petrochemical industry. separation at lower pressure and temperature follows and this pressure change can be used to drive a turbine. generator available heat flow for integration product Fig. Opencycle gas turbine power plants are widely applied throughout industry. p 2 3 working fuid C compressor +Δ p separator turbine −Δ p T G el. and will be presented individually. 3): • gas turbine (T) • heat exchanger (H) • separator (S). 3. The individual processes’ units in the open gas turbine system have their own importance. Open circuit gas turbine system The power cycle of the open gas turbine system is described as the “Brayton cycle”. generator 1 S 5 heat exchanger H 4 available heat flow for integration product Fig. The working fluid undergoes the following process steps. The open gas turbine is a basic gas turbine unit. 4): • 1−2 adiabatic compression • 2−3 reaction • 3−4 adiabatic expansion of reaction outlet stream in a turbine • 4−5 cooling or/and available heat flow for heat integration • 5 separation. as shown in a simplified T/s (temperature/mass entropy) diagram (Fig. The working fluid comes from the reactor and circulates through the following units (Fig. reactor R high T.Electricity Cogeneration using an Open Gas Turbine 111 The high operating pressure at the reactor’s outlet can be exploited to produce electricity using an open gas turbine. This turbine uses processed gas as a working fluid. . where the liquid product separates off and • compressor (C). after time t: ωr = dξ r /dt r = 1.S). It can be calculated if the equilibrium concentration of each reactant and product in a reaction at equilibrium is known. The thermodynamic and kinetic properties of the chemical reactions (r = 1.. The simplified temperature/mass entropy (T/s) diagram 3.. R) provide a good prediction about flow rate and the compositions of the raw material.. The amount flow rate from the reactor affects the power of the turbine. The conversion rate of reaction r (ωr) can be calculated from the differential change of the reaction extent (dξr). νCC +νDD where νs are stoichiometric coefficients. S) depends on the equilibrium constant (Ke). R (1) Any differential change in the reaction extent (dξr) can be calculated from the differential change in its amount (dns). …. 4..112 Gas Turbines T 3 2 5 1 4 s Fig. R (2) . which react at different reactions r (r = 1. in our case concentrating in particular. For the hypothetical reversible chemical reaction: νAA +νBB the equilibrium constant is defined as: Ke = cCν C ⋅ cDν D c Aν A ⋅ c Bν B .. …. and parameter conditions. S r = 1. and cs concentrations of components s. its conversion to a product.1 Reactor (R) The reactor processing unit for the production of various products. …. The equilibrium constant determines the extent of a chemical reaction at equilibrium. The high pressure reactor model is presented with all components s (s = 1.R). The amount flow rate (F) for any component (s = 1. and its stoichiometric coefficient (ν): dξr = dns /νs.r s = 1. …. …. on those that operate and produce under high pressures.. R r (4) The amount flow rate F is defined as: Fs = dns /dt and outlet amount flow rate for component s is: Fs. S   r = 1..R (3) and the outlet amount for component s for reaction r is: Fs.out ns. … . compressed pressure ratio and mass flow. … . … .. S (5) Σ vs. out ) ⋅ F Gas turbine power (Ptur) is a function of: • outlet temperature (Ttur. The medium pressure of the designed turbine can be varied. see Equation 9): Ptur = Cm ⋅ (Ttur.. 1987) can be calculated by the minimization of Gibbs (free) energy (ΔG): Kr = e(−ΔGr/RT) r = 1..r ∫ dξr 0 ξr s = 1.Electricity Cogeneration using an Open Gas Turbine 113 The extent of a reaction characterizes how far the advancement of the reaction has taken place. 3. 5). ….out = ns. S   r = 1.2 Turbine (T) The power of the gas turbine depends on the primary variables: inlet temperature.r ωr         s = 1. … . R (8) High reactant flow rate favours reactions with higher conversion and optimization of raw material composition and can increase production.in ∫ dns = vs. molar heat capacity (Cm) and the amount flow rate (F. Cogeneration is constrained by the lowest possible outlet temperature of the gas turbine.out: ns. out). which can enlarge electricity cogeneration and heat integration during a process (Fig.. R r (6) The total outlet amount flow rate (F) is: F = Σ Fs. This simultaneous approach can optimize the trade-off between heat and electricity cogenerations. …. thus cogeneration is usually more profitable than heat integration. in − T tur. Cogeneration chooses the lowest temperature limit. The inlet temperature is restricted by the metallurgical limit of the turbine’s blades to about 800 ºC. S  s (7) The equilibrium constant (Kr) of reaction r (Smith & Ness.out) (9) ..out        s = 1. The changing amount flow rate for reactant (ΔF) affects the heat flow rate of the outlet reaction stream (Φ).r ξr         s = 1. Equation 2 has to integrate from an initial ξr = 0 and ns = ns. … ... Its power (Ptur) is a function of the outlet temperature (Ttur.in to outlet ξr and ns. S r = 1.in + s = 1.in + Σ vs.out = Fs. in) is kept constant. 5.3 Heat exchanger (H) The residual heat in the heat exchanger (H) can usefully be applied to the heat integration. 1997): Cd. higher industrial costs.114 Gas Turbines T Φ/T relationship before Δ F Φ/T relationship after Δ F Lowest temperature limit of gas turbine outlet Cogeneration before ΔF HI before ΔF HI after Δ F Cogeneration after Δ F Φ Fig. The thermodynamic efficiency of the medium pressure turbine (ηtur) and the mechanical efficiency of the generator (ηgen) is supposed to be 85 % for each.. and cogeneration before and after ΔF. 3. determined by experience. Biegler et al. therefore.tur in EUR/a) is a function of the power (Ptur . molar heat capacity (Cm) • • amount flow rate (F) The inlet temperature (Ttur. (11) . by using equation 11: (TinH − ToutH) ⋅ CFH = ΦH where CFH is the heat capacity flow rate of the stream in heat exchanger. tur = (22 946 + 13. the costs are multiplied by a factor (4). The annual depreciation of the medium pressure turbine (Cd.5 ⋅ Ptur) ⋅ 4 (10) The published cost equations for the equipment are not usually adjusted to the real. The simplified temperature/heat flow rate (T/Φ) diagram before and after changing the flow rate (ΔF) of the raw material: performing heat integration (HI). The heat flow (Φ) can be calculated with known inlet (TinH) and outlet temperatures (ToutH). see Equation 12)..ls s = 1. using different methods. and can be calculated by the equation: Toutc = ac + bc ⋅ Tinc (18) where ac and bc are the temperature constants for polytropic compression. Equation 13 includes the amount flow fractions.l . MINOS).S) are: Fin = Fout.l ·xout. The parameters in the model of an open gas turbine were simultaneously optimized using the GAMS/MINOS (Brooke at al. Once we know.v) and liquid phases (Fout. complex processes.l s = 1 s S (15) s = 1. g. The temperatures at the outlets of the compressor (Toutc.Electricity Cogeneration using an Open Gas Turbine 115 3. 4. The NLP model contains variables of all those process’ . the whole model of the open gas turbine system can be optimized. The equilibrium constant (K) of the sth component during separation is a function of temperature (see Equation 16).l Fin·xins = Fout..4 Separator (S) The separator has the task of separating liquid from the vapour phase. Vapour flow is compressed in the compressor (C).v + Fout. This NLP can be solved using a large-scale reduced gradient method (e. S (17) The inlet amount flow rate for separation (Fin) is the sum of the outlet amounts flow rates of the vapour (Fout. it does not guarantee a global optimization solution but it quickly gives good results for non-trivial. depend on the inlet temperatures (Tinc).vs = Ks⋅ xout. …. 3. The model is nonconvex. S (12) (13) (14) Σ x out..v ·xout. Case study The suggested open gas turbine system was tested in an existing complex.ls s = 1. 1997). cs and bs are equilibrium constants during separation xout.. Biegler et al. 1992). The product is in liquid phase. low-pressure Lurgi methanol plant producing crude methanol by using nonlinear programming (NLP.5 Compressor (C) Vapour flow from the separator is compressed within the compressor (C). ….vs = 1 s S Σ x out. S (16) Ks = ds + cs ⋅ Tout + bs ⋅ (Tout)2 where ds. x is the amount fraction in vapour (v) or liquid phase (l). The balanced amounts of the separation for all the components (s = 1.vs + Fout. …. 7 MW of heat flow rate are exchanged with the existing areas. 6.1 MW and 4. The integrated process streams in HEPR. air 12.5 MW of high pressure steam HEW1 41 bar COMP1 2 MW 35 bar 49.8 MW new heat exchanger HEST 16.7 MW of electricity cogeneration REA purge decreasing purge gas flow rate to 190 mol/s crude methanol 0. This structure enables the generation of 12. using a open gas turbine system . heat flow rates. out = 110 oC (Fig.75 mol/s of aditional methanol production Fig.116 Gas Turbines parameters: molar heat capacities. The HEW1 exchanges 2.75 mol/s. HEW and HEA 7.5 MW of heat flow rate. 6). The additional annual of methanol production is 0. respectively. The power of the first and the second compressors are 2. respectively.0 MW. Optimised flow sheet for crude methanol production. and temperatures.W. material flow rates. 4. and the optimization selected for electricity generation using a gas turbine pressure drop from 49.5 bar TUR HEW SEP 35 bar HEA 35 bar 110 oC C.7 bar to 35 bar with an outlet temperature of Ttur.8 MW. The steam exchanger (HEST) needs 16. exchange 3. which are limited by real constraints.7 MW of electricity. Within the heat exchangers. 3.6 MW of heat flow rate. purge gas outlet flow rate is decreased from 210 mol/s to 190 mol/s. when cooling.6 MW of heat exchange HEPR 51 bar new two-stage compressor COMP2 2.1 Results The simultaneous NLP of heat and power integration.0 MW and 2. E. & Meeraus. 4 kEUR/a for the maintenance cost (estimated as 2 % of the additional direct plant cost).5 ⋅ 2 # Installed cost of compressor. A. and the compressor. The additional annual income of the methanol produced is 79 kEUR/a. The working fluid comes from the reactor and circulates through the process units: gas turbine. Prentice Hall.2 * Tjoe and Linnhoff.. 10 kEUR/a for the contingency (estimated at 5 % of the additional direct plant cost). Installed cost of heat exchanger*/EUR: (8 600 + 670 A0. Kendrick D.4 Cost of 37 bar steam (C37)**/(EUR/(kW ⋅ a)): 106. A = area in m2 ** Swaney. L. & Westerberg. Systematic methods of chemical process design. 1986.. A. 8. heat exchanger. GAMS: A User’s Guide. The additional annual income of the electricity produced is 5 530 kEUR/a. I. is 2 040 kEUR/a (Table 1).3 Cost of cooling water (CCW)**/(EUR/(kW ⋅ a)): 6.Electricity Cogeneration using an Open Gas Turbine 117 The additional annual depreciation of the gas turbine. New Jersey. Conclusion The inclusion of open gas turbine can increase the operating efficiency of the process. Grossmann. Cost items for example process 7. higher industrial costs using multipliers (2 or 4). The cost of the high pressure steam used in HEST is 1 750 kEUR/a. Upper Saddle River. Palo Alto. (1992). separator (where the liquid product separates). HEW1. . W. Brooke. and the new two-stage compressor. having areas of 527 m2 and 324 m2). Ccom&/EUR: 2 605 ⋅ P0. A. 1989 & Biegler et al. and 15 kEUR/a for the turbine down time (estimated as 5 % of the additional plant direct cost).82 Installed cost of gas turbine. we included additional costs to the new units only: 30 kEUR/a for the instrumentation cost (which is estimated to be 15 % of the additional direct plant cost). The additional profit from process and power integration is estimated to be 1 760 kEUR/a for the modified process. 1−408. References Biegler.83) ⋅ 3. The gas turbine with its pressure and temperature drop can be included in the process cycle. Table 1. (1997). Scientific Press. 1997.0 Price of electricity (Cel)**/(EUR/(kW ⋅ a)): 435. T. new heat exchangers (HEST. In the depreciation account for retrofit.. Ctur&/(EUR/a): (22 946 + 13.5 Ptur) ⋅ 4 # Price of methanol (CM) +/(EUR/t): 115. P = power in kW + ten years average # published cost equations for the equipment are adjusted to the real. B. AIChE Journal 35/6. Tjoe. New York. 1010. & Van Ness. H. Thermal integration of processes with heat engines and heat pumps. T. J. McGraw-Hill. Engng 28 47−60.118 Gas Turbines Smith. Chem. (1987). 496−518. R. Introduction to chemical engineering thermodynamics. Using pinch tehnology for process retrofit. Swaney. (1986). . N. (1989). & Linnhoff. pp.M.C. compressing. various power plants and industrial and manufacturing processes. In order to keep reliability high. Development of communication techniques. Success of monitoring not only depends on perfection of monitoring hardware and software themselves. Being capable to detect and identify incipient faults. communication techniques.6 Gas Turbine Condition Monitoring and Diagnostics National Polytechnic Institute Mexico 1. and suitable access to the diagnostic results. various diagnostic tools are applied. fast data processing. In these centres great volume of data can effectively be analyzed by qualified personnel.) in order to realize self-diagnostics. Various deterioration factors can be responsible for these failures. pressure. health monitoring has become an important and rapidly developing discipline which allows effective machines maintenance. oil debris. In these conditions. sensors become more and more “intelligent” or “smart”. Considerable increase of industrial accidents and disasters has been observed in the last decades (Rao. in particular. they reduce the rate of gross failures. So. aircrafts. and computer technology. noise. Introduction Gas turbine monitoring and diagnostics belong to a common area of condition monitoring (health monitoring) of machinery and mechanical equipment such as spacecrafts. shock. etc. Large numbers of powerful PCs united in networks allow easy sharing the measured data through the company. In two last decades the development of monitoring tools has been accelerated by advances in information technology. heat. 1996). corrosion. flow. 1996). They can be considered as complex engineering systems and become more sophisticated during their further development that results in potential degradation of system reliability. The personal computer has radically changed as well. shipboard systems. wireless technologies drastically simplifies data acquisition in the sites of machine operation. and speed (Rao. Behind this trend lies a well Igor Loboda . but also is determined by tight monitoring integration with maintenance when the both disciplines can be considered as one multidiscipline. in instrumentation. humidity. rain. and decrease volume of data for subsequent processing. dust. reduce measurement errors. Mechanical failures cause a considerable percentage of such accidents. Modern sensors trend to preliminary signal processing (filtering. cold. Development of the PC technology also allows many independent disciplines to be integrated in condition monitoring. the most common factors that degrade a healthy condition of machines are vibration. particularly. Data transmission to centralized diagnostic centres is also accelerated. Among them. 120 Gas Turbines known concept of Condition Based Maintenance (CBM) as well as ideas of Condition Monitoring and Diagnostic Engineering Management (COMADEM) (Rao, 1996) and Prognostics and Health Management (PHM) (Vachtsevanos et al., 2006). As illustrated by many examples in (Rao, 1996), the proper organization of the total monitoring and maintenance process can bring substantial economical benefits. Numerous engineering systems, which considerably differ in nature and principles of operation, need individual techniques in order to realize effective monitoring. The variety of known monitoring techniques can be divided into five common groups: vibration monitoring, wear debris analysis, visual inspection, noise monitoring, and environment pollution monitoring (Rao, 1996). The two first approaches are typical for monitoring rotating machinery, including gas turbines. A gas turbine engine can be considered as a very complex and expensive machine. For example, total number of pieces in principal engine components and subsystems can reach 20,000 and more; heavy duty turbines cost many millions of dollars. This price can be considered only as potential direct losses due to a possible gas turbine failure. Indirect losses will be much greater. That is why, it is of vital importance that the gas turbine be provided by an effective monitoring system. Gas turbine monitoring systems are based on measured and recorded variables and signals. Such systems do not need engine shutdown and disassembly. They operate in real time and provide diagnostic on-line analysis and recording data in special diagnostic databases. With these databases more profound off-line analysis is performed later. The system should use all information available for a diagnosed gas turbine and cover a maximal number of its subsystems. Although theoretical bases for diagnosis of different engine systems can be common, each of them requires its own diagnostic algorithms taking into account system peculiarities. Nowadays parametric diagnostics encompasses all main gas turbine subsystems such as gas path, transmission, hot part constructional elements, measurement system, fuel system, oil system, control system, starting system, and compressor variable geometry system. In order to perform complete and effective diagnosis, different approaches are used for these systems. In particular, the application of such common approaches of rotating machinery monitoring as vibration analysis and oil debris monitoring has become a standard practice for gas turbines. However, the monitoring system always includes another technique, which is specific for gas turbines, namely gas path analysis (GPA). Its algorithms are based on a well-developed gas turbine theory and gas path measurements (pressures, temperatures, rotation speeds, and fuel consumption, among others). The GPA can be considered as a principal part of a gas turbine monitoring system. The gas path analysis has been chosen as a representative approach to the gas turbine diagnosis and will be addressed further in this chapter. However, the observations made in the chapter may be useful for other diagnostic approaches. The gas path analysis provides a deep insight into gas turbine components’ performances, revealing gradual degradation mechanisms and abrupt faults. Besides these gas path defects, malfunctions of measurement and control systems can also be detected and identified. Additionally, the GPA allows estimating main engine performances that are not measured like shaft power, thrust, overall engine efficiency, specific fuel consumption, and compressor surge margin. Important engine health indicators, the deviations in measured variables induced by engine deterioration and faults, can be computed as well. Gas Turbine Condition Monitoring and Diagnostics 121 The gas path analysis is an area of extensive studies and thousands of technical papers can be found in this area. Some common observations that follow from these works and help to explain the structure of this chapter are given below. First, it can be stated that gas turbine simulation is an integral part of the diagnostic process. The models fulfil here two general functions. One of them is to give a gas turbine performance baseline in order to calculate differences between current measurements and such a baseline. These differences (or deviations) serve as reliable degradation indices. The second function is related to fault simulation. Recorded data rarely suffice to form a representative classification because of the rare and occasional appearance of real faults and very high costs of real fault simulation on a test bed. That is why mathematical models are involved. The models connect degradation mechanisms with gas path variables, assisting in this way with a fault classification that is necessary for fault diagnosis. Second, a total diagnostic process can be divided into three general and interrelated stages: common engine health monitoring (fault detection), detailed diagnostics (fault identification), and prognostics (prediction of remaining engine life). Since input data should be as exact as possible, an important preliminary stage of data validation precedes these principal diagnostic stages. In addition to data filtration and averaging, it also includes a procedure of computing the deviations, which are used practically in all methods of monitoring, diagnostics, and prognostics. Third, gas turbine diagnostic methods can be divided into two general approaches. The first approach employs system identification techniques and, in general, so called thermodynamic model. The used models relate monitored gas path variables with special fault parameters that allow simulating engine components degradation. The goal of gas turbine identification is to find such fault parameters that minimize difference between the model-generated and measured monitored variables. The simplification of the diagnostic process is achieved because the determined parameters contain information on the current technical state of each component. The main limitation of this approach is that model inaccuracy causes elevated errors in estimated fault parameters. The second approach is based on the pattern recognition theory and mostly uses data-driven models. The necessary fault classification can be composed in the form of patterns obtained for every fault class from real data. Since patterns of each fault class are available, a data-driven recognition technique, for example, neural network, can be easily trained without detailed knowledge of the system. That is why, this approach has a theoretical possibility to exclude the model (and the related inaccuracy) from the diagnostic process. Fourth, the models used in condition monitoring and, in particular, in the GPA can be divided into two categories – physics-based and data-driven. The physics-based model (for instance, thermodynamic model) requires detailed knowledge of the system under analysis (gas turbine) and generally presents more or less complex software. The data-driven model gives a relationship between input and output variables that can be obtained on the basis of available real data without the need of system knowledge. Diagnostic techniques can be classified in the same manner as physics-based or model-based and data-driven or empirical. Illustrating the above observations, Fig. 1 presents a classification of gas path analysis methods. Taking into the account the observations and the classification, the following topics will be considered below: real input data for diagnosis, mathematical models involved, preliminary data treatment, fault recognition methods and accuracy, diagnosis and monitoring interaction, and application of system identification methods for fault diagnosis. 122 GPA techniques Gas Turbines Stages of diagnostic process Data validation, deviations Monitoring Theoretical bases System identification Pattern recognition Models used Physics -based Data -driven Diagnostics Prognostics Fig. 1. Classification of gas path analysis techniques 2. Diagnostic models 2.1 Nonlinear static model In the GPA the physics-based models are presented by thermodynamic models for simulating gas turbine steady states (nonlinear static model) and transients (nonlinear dynamic model). Since the studies of Saravanamuttoo et al., in particular, (Saravanamuttoo & MacIsaac, 1983), application of the thermodynamic model for steady states has become common practice and now this model holds a central position in the GPA. Such a model includes full successive description of all gas path components such as input device, compressor, combustion chamber, turbine, and output device. Such models can also be classified as non-linear, one-dimensional, and component-based. The thermodynamic model computes a (m×1)-vector Y of gas path monitored variables as a function of a vector U of steady operational conditions (control variables and ambient conditions) as well as a (r×1)-vector Θ of fault parameters, which can also be named health parameters or correction factors depending on the addressing problems. Given the above explanation, the thermodynamic model has the following structure: Y = F(U , Θ) . → → → (1) There are various types of real gas turbine deterioration and faults such as fouling, tip rubs, seal wear, erosion, and foreign object damage whose detailed description can be found, for example, in the study (Meher-Homji et al., 2001). Since such real defects occur rarely during maintenance, the thermodynamic model is a unique technique to create necessary class descriptions. To take into account the component performance changes induced by real Gas Turbine Condition Monitoring and Diagnostics 123 gradual deterioration mechanisms and abrupt faults, the model includes special fault parameters that are capable to shift a little the components’ maps. Mathematically, the model is a system of nonlinear algebraic equations reflecting mass, heat, and energy balance for all components operating under stationary conditions. The thermodynamic model represents complex software. The number of algebraic equations can reach 15 and more and the software includes dozens of subprograms. The most of the subprograms can be designed as universal modules independent of a simulated gas turbine, thus simplifying model creation for a new engine. System identification techniques can significantly enhance model accuracy. The dependency Y = f 1 (U ) realized by the model can be well fitted and simulation errors can be lowered up to a half per cent. Unfortunately, it is much more difficult to make more accurate the other dependency Y = f 2 (Θ) because faults rarely occur. The study presented in (Loboda & Yepifanov, 2010) shows that differences between real and simulated faults can be visible. As mentioned before, the thermodynamic model for steady states has wide application in gas turbine diagnostics. First, this model is used to describe particular faults or complete fault classification (Loboda et al., 2007). Second, the thermodynamic model is an integral part of numerous diagnostic algorithms based on system identification such as described in (Pinelli & Spina, 2002). Third, this nonlinear model allows computing simpler models (Sampath & Singh, 2006), like a linear model (Kamboukos & Mathioudakis 2005) described below. 2.2 Linear static model The linear static model present linearization of nonlinear dependency Y = f 2 (Θ) between gas path variables and fault parameters determined for a fixed operating condition U . The model is given by a vectorial expression δ Y = Hδ Θ . (2) It connects a vector δ Θ of small relative changes of the fault parameters with a vector δ Y of the corresponding relative deviations of the monitored variables by a matrix H of influence coefficients (influence matrix). Since linearization errors are not too great, about some percent, the linear model can be successfully applied for fault simulation at any fixed operating point. However, when it is used for estimating fault parameters by system identification methods like in study (Kamboukos & Mathioudakis, 2005), estimation errors can be significant. Given the simplicity of the linear model and its utility for analytical analysis of complex diagnostic issues, we can conclude that this model will remain important in gas turbine diagnostics. The matrix H can be easily computed by means of the thermodynamic model. The gas path variables Y are firstly calculated by the model for nominal fault parameters Θ0 . Then, small variations are introduced by turns in fault parameters and the calculation of the variables Y is repeated for each corrected parameter. Finally, for each pair Yi and Θ j the corresponding influence coefficient is obtained by the following expression H ij = δ Yi Yi (Θ j ) − Yi (Θ0 ) = δΘ j Yi (Θ0 ) Θ j − Θ0 j Θ0 j . (3) 124 Gas Turbines 2.3 Nonlinear dynamic model Although methods to diagnose at steady states are more developed and numerous than the methods for transients, current studies demonstrate growing interest in the gas turbine diagnosis during dynamic operation (Loboda et al., 2007; Ogaji et al., 2003). A thermodynamic gas path model (dynamic model) is therefore in increasing demand. As distinct from the static model (1), in the dynamic model a time variable t is added to the argument set of the function Y and the vector U is given as a time function, i.e. a dynamic model has a structure Y = F(U (t ), Θ , t ) . → → → (4) A separate influence of time variable t is explained by inertia nature of gas turbine dynamic processes, in particular, by inertia moments of gas turbine rotors. The gas path parameters Y of the model (4) are computed numerically as a solution of the system of differential equations in which the right parts are calculated from a system of algebraic equations reflecting the conditions of the components combined work at transients. These algebraic equations differ a little from the static model equations, that is why the numeric procedure of the algebraic equation system solution is conserved in the dynamic model. Therefore, the nonlinear dynamic model includes the most of static model subprograms. Thus, the nonlinear static and dynamic models tend to be united in a common program complex. 2.4 Neural networks Artificial Neural Networks (ANNs) present a fast growing computing technique in many fields of applications, such as pattern recognition, identification, control systems, and condition monitoring (Rao, 1996; Duda et al., 2001). The ANN can be classified as a typical data-driven model or black-box model because it is viewed solely in terms of its input and output without any knowledge of internal operation. During network supervised learning on the known pairs of input and output (target) vectors, weights between the neurons change in a manner that ensures decreasing a mean difference (error) e between the target and the network output. In addition to the input and output layers of neurons, a network may incorporate one or more hidden layers of nodes when high network flexibility is necessary. The multilayer perceptron (MLP) has emerged as the most widely used network in gas turbine diagnostics (Volponi et al., 2003). Its foundations can be found in any book devoted to ANNs and we give below only a brief perceptron description. The MLP is a feed-forward network in which signals propagate through the network from its input to the output with no feedback. The diagram shown in Fig.2 helps to understand better perceptron operation. The presented network includes input, hidden, and output layers of neurons. For each hidden layer neuron, the sum of inputs of a vector p multiplied by waiting coefficients of a matrix W1 is firstly computed. The corresponding bias from a vector b1 is added then, forming a neuron input. Finally, inputs of all neurons are transformed by a hidden layer transfer function f2 into an output vector a 1 . The described procedure can be written by the following expression → a 1 = f 1 ( W1 p + b 1 ) . → → (5) Gas Turbine Condition Monitoring and Diagnostics 125 Fig. 2. Perceptron diagram The same procedure is then repeated for the output layer considering a 1 as an input vector. Similarly to formula (5), the output layer is given by → y = a 2 = f 2 ( W2 a 1 + b 2 ) . → → → (6) Before the use the network should be trained on known pairs of the input vector and the output vector (target) in order to determine unknown waiting coefficients and biases. The MLP has been successfully applied to solve difficult pattern recognition problems since a back-propagation algorithm had been proposed for the training. It is a variation of so called incremental or adaptive training mode that changes unknown coefficients after presentation of every individual input vector. In the back-propagation algorithm the error between the target and actual output vectors is propagated backwards to correct the weights and biases. The correction is repeated successively for all available inputs and targets united in a training set. Usually it is not sufficient to reach a global minimum between all targets and network outputs and a cycle of calculations with learning set data is repeated many times. That is why this algorithm is relatively slow. To apply the back-propagation algorithm, a layer transfer function should be differentiable. Generally, it is the tan-sigmoid, log-sigmoid, or linear type. There is another training mode called a batch mode because a mean error e between all network targets and outputs is computed and used to correct the coefficients. In this mode the training comes to a common nonlinear minimization problem in which the error e( W 1 , b 1 , W 2 , b 2 ) should be minimized in a multidimensional space of all unknown coefficients, waits and biases. This error can be reduced but should not be vanished because the network must follow general systematic dependencies between simulated variables and should not reflect individual random errors of every input and output. Though the trained network is ready for practical use in a gas turbine diagnosis, an additional stage of network verification is mandatory. There is a common statistical rule that 126 Gas Turbines a function determined on one portion of the random data should be tested on another. Consequently, to verify the MLP determined on a training set, we need one more data portion called a validation set. If the neural network describes well training data but loses its accuracy on validation data it is a clear indication of an overlearning effect. The network begins to take into account training set random peculiarities and therefore loses its capability to generalize data. In addition to the MLP described above, some other network types are also used in the gas path analysis, in particular, Radial Basis Networks, Probabilistic Neural Networks (Romessis & Mathioudakis, 2003; Romessis et al., 2007), and Bayesian Belief Networks (Romessis & Mathioudakis, 2006; Romessis et al., 2007). Foundations of these particular recognition and approximation tools can be found in any book in the area of ANNs, for instance, in (Haykin, 1994). The language of technical computing MATLAB developed by the MathWorks, Inc. offers convenient tools to experiment with different neural networks. It contains a neural networks toolbox that simplifies network creation, training, and use. MATLAB also allows choosing between various training functions and calculation options. With respect to diagnostic problems where the ANNs are used, it can be concluded that in most cases networks are employed for gas turbine fault identification, in particular, to form fault classification (Ogaji et al., 2003) and to estimate fault parameters (Romessis & Mathioudakis, 2006). However, the ANNs not only are applied for recognition problems, but they also are famous as good function approximators in many fields including gas turbine monitoring (Fast et al., 2009). In addition to ANNs, other and simpler data-driven models like polynomials can be successfully applied to simulate gas turbine performances. 2.5 Polynomials It is proven in (Loboda et al., 2004) that complete second order polynomials give sufficient approximation of healthy engine performance (baseline). For one monitored gas path variable Y as a function of three arguments ui, such polynomial is written as 2 2 2 Y0 (U ) = a0 + a1u1 + a2 u2 + a3u3 + a4 u1u2 + a5u1u3 + a6u2 u3 + a7 u1 + a8u2 + a9 u3 . (7) The polynomials for all monitored variables can be given in the following generalized form: T Y0 = V T A , → → (8) → T where is a (1×m)-vector of monitored variables, V is a (1×k)-vector of components 2 2 1, u1 , u2 ,...u2 , u3 , and A presents a (k×m)-matrix of unknown coefficients ai for all m monitored variables. Since measurements at one steady-state operating point are not sufficient to compute the coefficients, data collected at n different points are included into the training set and involved into calculations. With new matrixes Y (n×m) and V (n×k) formed from these data, equation (8) is transformed in a linear system Y = VA . → T Y0 (9) ˆ To enhance estimations ai , large volume n>>k of input data is involved and the leastsquares method is applied to solve system (9), resulting in the well known solution: also known as residuals and deltas.m is computed in a relative form δ Yi* = Yi* − Y0 i (U ) Y0 i (U ) → → . Since success of all principal diagnostic stages directly depends on the deviations’ quality. A compressor washing at the time point t = 7970 as well as fouling periods before and after the washing are well-distinguishable in the figure. we will return to polynomials and other described above models considering their particular applications in the GPA methods. a total gas turbine diagnostic process usually includes a preliminary procedure of computing deviations. To draw useful diagnostic information from raw recorded data. In the below sections that describe the stages of a total diagnostic process.1 Deviations Modern instrumentation and data recording tools allow collecting a great volume of test bed and field data of different types. are defined as differences between measured and engine baseline values. it can be written as function Y0 (U ) usually called a baseline function or model. Every measurement section (snapshot) includes engine operational conditions U . Let us call this engine GT1. . When recorded over a long period of time. or hour) at steady states.5 thousand hours. With this model the deviations for each monitored variables Yi . averaged. Figure 3 exemplifies the exhaust gas temperature (EGT) deviations of a gas turbine for natural gas pumping stations. The deviation consists of the systematic influence (signal) induced by engine degradation or faults and a noise component. When properly computed. the presented data cover approximately 4. the deviations can have relatively high quality (signal-to-noise ratio) and can potentially be good indicators of engine health. Typically. which set an engine operating point. ∧ (10) As can be seen. The deviations. day. and monitored variables Y . historical engine sensor data are used in diagnostics that were previously filtered. As can be seen. The most common cause of stationary gas turbines’ deterioration is compressor fouling and the data with fouling and washing cycles are widely used in order to verify diagnostic techniques.Gas Turbine Condition Monitoring and Diagnostics 127 A = ( VT V )−1 VT Y . and periodically recorded (once per flight. these snapshots can provide valuable information about the deterioration and faults. best efforts should be applied to keep deviation errors to a minimum. 3. By direct analysis of the variables themselves it is difficult to discriminate performance degradation effects from great changes due to different operating modes. The deviations are plotted here against an operation time t (here and below a variable t is given in hours). As the baseline depends on an engine operating condition.i = 1. The deviations δ Y * computed on real measurements with noise are marked by a grey colour while a black line denotes ideal deviations δ Y without noise. Data validation and preliminary processing 3. polynomials present a typical data-driven model because only input and output data are used to compute polynomials’ coefficients. (11) where Yi* denotes a measured value. which is explained by sensor errors and a baseline model inadequacy. (12) where σ (ε Σ ) is a standard deviation of the errors. To enhance the quality we should reduce the errors ε Σ . and δ 3 . It was found in (Loboda & Santiago. 3. 3. Additional plots like the time plot of some parallel measurements of the same variable assist to identify the problem. If we designate the maximum deviation δ Y as δ 0 . there are three elemental errors given here by error intervals δ 1 .8%. Let us analyse separately these error sources. Total error ε Σ consists correspondingly of three components and can be given by the formula: εΣ = ε1 + ε2 + ε3 . According to Fig.2 Sensor malfunction detection Developed graphical tools of monitoring systems can promote a successful exploration of abnormal sensor behaviour. Some examples of sensor malfunctions revealed by the described graphical tools are given below. However.3. 2001) that great outliers δ3 at the end of the analysed time interval of Fig. and ε 3 means single outliers with the amplitude greater than 0. different deviation plots can be applied because the deviations are very sensitive to sensor errors.128 Gas Turbines Fig. (13) where ε 1 is a normal noise smaller than 0. Deviations' characteristics A difference ε Σ = δ Y * − δ Y can be considered as an error. the signal-to-noise ratio δ 0 = δ 0 σ (ε Σ ) .8%. ε 2 presents slower fluctuations of the amplitude limited by 0. As a result of numerical analysis it was found that the inlet temperature error influences . δ 2 .3 are related with wrong measurement of a gas turbine inlet temperature tin. will be an index of diagnostic quality of the deviations δ Y * . In particular.2% that is observed at every time point. these plots can not sometimes explain a true cause of detected abnormal fluctuations in the deviations. The errors can be induces by both sensor malfunctions and baseline model inadequacy. For special cases theoretical analysis can also be applied to make clear the origin of the fluctuations. The explanation is that an abnormal increase in the variable Tin. Another example of input temperature sensor errors is described in (Loboda et al. 4. GT2 inlet temperature sensor faulty operation The next example of sensor data anomalies is related with a fuel consumption. the TH curve changes a little but the Tin curve shows frequent spikes and shifts that are synchronous with anomalies in the dTt curve. similar prolonged shifts in the consumption deviations were also revealed.Gas Turbine Condition Monitoring and Diagnostics 129 the deviations according to the following mechanism: [increasing of temperature tin due to the errors] → [drop of the calculated value of a corrected rotation speed] → [reducing an inlet guide vane angle by the control system] → [gas flow decreasing and the corresponding power drop below the setting level] → [feeding the additional fuel by the control system to reach the power setting] → [the increase of gas path variables due to the compressor condition change and the regime raising] → [deviation increase]. Figure 5 helps to verify . 2009). Let us call this engine GT2. which is a baseline function argument. which can be regarded as one of the most important variables for control and monitoring systems. results in a function increment for all monitored temperatures and the corresponding fall in the deviations dTt. 2009).. As can be seen. In fuel consumption deviations dGf computed for one of the units of the GT2. Analyzing data from two other units. an unusual decrease of approximately 7% over a prolonged period of time was found and described in (Loboda et al. Figure 4 illustrating this case presents the plots of the variables Tin and TH and EGT deviations dTt.. The idea arose about a possible common cause of the consumption deviation shifts in different gas turbine units. It was found in the data recorded in a gas turbine driver for an electric generator. Fig. Such errors are capable to hide degradation and fault effects completely and to render useless gas turbine monitoring. which is about -5%. Thus. the input temperature errors resulted in wrong control system operation and undesirable EGT increase. The deviation shifts are well visible from the end of January to the beginning of April and they begin and end at the same time for different units. can also be useful to detect sensor problems. What reasonable explanation can there be to the puzzling fact that independent fuel consumption sensors have a common source of errors? The answer was related with a variable chemical structure of fuel gas supplied from a common source that produces synchronous fluctuations of a gas calorific value in the units. Graphs (a) and (b) in Fig. a – unit 3) The described above cases of sensor abnormal behaviour were found with the use of deviation plots. some cases of single thermocouple probe faults have been found. Fig. Opposite spike directions in the graphs probably indicate different thermocouple fault origins. parallel measurements of the same variable. a suite of thermocouple probes installed in a high pressure turbine discharge station of the GT2. Observing two 25% spikes in graph (a) and a 50% spike in graph (b). for example.130 Gas Turbines this idea. a – unit 2. Fuel consumption deviations vs. a calendar time for all three units. Although the thermocouple data were filtered and averaged before recording. calendar time (a – unit 1. The deviations dGf are plotted here vs. 6 illustrate them. 5. . we can conclude with no doubt that they are results of probe faults. The outliers are well visible in the figure and the used filtering algorithm should be modified to exclude them. Nevertheless. On the one hand.. the deviation quality can be enhanced by the sensor malfunction detection and data cleaning from wrong data. unit 1. Moreover. to satisfy approximation requirements. In the first method. a technological process requires certain gas turbine power and does not allow arbitrary changes of an operating point. To demonstrate the possibility and advantages of the baseline model created on the basis of the thermodynamic model (see Loboda et al. unit 3 In this way. 3. the baseline model is not adequate at the operating conditions not presented in the learning set. b – a single gross error. the learning set must incorporate extensive data collected at all possible operating conditions. Two described below methods overcome mentioned difficulties. 6. two learning set variations are formed. As a result.3 Baseline model improvement The baseline model adequacy considerably depends on the learning set but the problem to compose a proper set for model determination seems to be challenging. The next mode to improve deviations is to make the baseline model as adequate as possible. Variation 1. On the other hand. EGT probes' errors: a – single gross errors. data collection period is limited by a short time when a gas turbine condition can be considered as healthy and invariable.Gas Turbine Condition Monitoring and Diagnostics 131 a) b) Fig. the thermodynamic model is applied. The learning set is created from 694 consecutive recorded operating points of the . 2004). Thus. As can be seen. the use of the thermodynamic model can be recommended.nPT . the learning set points occupy only two limited zones of the operating space “Gf . 7.7b one can see the advantages of such a model based learning set: the points are uniformly distributed in a much greater zone than in the case of real data. On the basis of the described data sets two corresponding polynomial baseline models have been calculated as explained in section 2. the model based learning set allow computing the deviations with notably lower errors. Fig. Variation 2. b – model based learning set) . 8. b – thermodynamic model data) a) b) Fig. it is suggested to apply the thermodynamic model for learning set generation. The learning sample includes 270 operating points generated by the thermodynamic model.132 Gas Turbines GT1. To overcome this obstacle. Figure 8 illustrates these two series of the EGT deviations and helps to compare two concerned modes to calculate the baseline model. As can be seen in the Fig. With the help of Fig.TH” (nPT denotes power turbine rotation speed). The deviations were computed then for each model and with the same real data that are shown in Fig.7a.3. Learning set points (a – real data. EGT deviations (a – data based learning set.2. The resulting baseline model is then determined by averaging the particular baseline functions. 2009). 9.Gas Turbine Condition Monitoring and Diagnostics 133 The second method overcoming the learning set difficulties is related with a degraded engine model (Loboda et al. Unit 1 power turbine temperature deviations for two methods of baseline model computation (a . With the baseline model found in this way. → → (14) Once computed. t ) = Y0 (U m ) + c15 t + c16 t 2 .9. Consequently.averaged model with the use of a time variable) . the data recorded in unit 1 of the GT2 during the second and third periods of fouling (1800 points in total) have been included in the learning set. from which the necessary baseline model can be derived. The method can be further improved. the idea of a degraded engine model seems to be promising for computing the deviations in practice. the degraded engine model can be given by Y (U m . To examine the idea. Fig. all recorded data could be used to compute unknown coefficients. b . Consequently. such model can be easily transformed into the necessary baseline model by putting t equal to zero. Since model (14) takes into consideration a varying deterioration level. the deviations were computed then for all available unit 1 data and considerable deviation enhancement was achieved. To that end.. for each analyzed fouling period a particular model of a degraded engine is computed using all data recorded during the period. Since a compressor fouling severity depends on the engine operation time t after the last washing. it is natural to add this variable to the arguments of the baseline function (7) in order to describe a degraded engine.model determined with 200 successive operating points. Traditional and new methods for baseline model formation are illustrated in Fig. One can see significant deviation improvement provided by the new method. 27 0. the baseline model allows to change parameters setting an operating point (function arguments).08 0. The results are given in Table 1.67 0.33 0.108 0.08 0.08 0.14 0.15 0.36 0.12 0.18 0.10 0. the variable nhp of high pressure rotor speed measured with high accuracy could be the best argument..15 1. .216 0.12 0. 2009) and an aircraft engine (Volponi et al. which contains averaged errors of each deviation and their mean number presented for all possible arguments and ranged according to this mean number.09 0. polynomials and the least square method have successfully been applied.11 0. Argument TТ TPT PC PТ Gf TC nhp Nе Deviations TТ TPT 0.74 0.143 0. but also is defined by its influence on the gas turbine behaviour which is great for the parameter nhp.21 1.45 0.25 Nе 0.20 6. 2010) verifies whether the application of such a powerful modelling tool as artificial neural networks (ANN) instead of polynomials yields higher adequacy of the baseline model and better quality of the corresponding deviations.17 0.11 0. The resulting model adequacy was sufficient for reliable monitoring gas turbine deterioration effects.66 0. The variety of analyzed neural network structures were considered and extensive field data of two different gas turbines were involved to compute and validate both techniques in order to draw sound conclusions on the network applicability to approximate healthy engine performance.11 0.01 TC 0.16 0. this study shows that a polynomial baseline model can be successfully used in real monitoring systems instead of neural networks. The explanation is that argument quality not only depends on its measurement accuracy. At least. At the first glance. The paper (Loboda & Feldshteyn. 2007).17 0.16 0.42 PТ 0. Thus. no manifestations of network superiority were detected.26 1.31 0.19 0.51 1.92 0. However.69 Gf 0.167 0.12 0. Deviation errors for different arguments In all described above methods improving the baseline model.13 0. Nevertheless. it seems to be true for simple cycle gas turbines with gradually changed performance.18 0. like the turbines considered in the study.12 0. polynomials were better in accuracy and.08 0. In a part of the considered cases. The numeric experiment has been conducted with the GT1 real data included 2608 operating points. The growing network application in gas turbine monitoring on the one hand and. in the other cases the compared techniques were practically equal.224 Table 1. 2004) can also improve the deviations..19 1. on the other hand. However.07 0.10 0.11 PC 0. Investigations report wide use of artificial neural networks as a tool to describe an engine baseline.29 - mean 0. This gives the possibility to examine all measured variables as such parameters.13 0.157 0.. for a stationary gas turbine (Fast et al. our own positive experience with the use of polynomials have encouraged us to conduct a thorough comparative study of these two techniques.39 0.17 0.36 1. Unlike a real engine.86 0. artificial neural networks are also famous as good function approximators in many fields including gas turbine monitoring.134 Gas Turbines Choosing the best baseline function arguments (Loboda et al. for example.11 0.41 nhp 0.08 0. it can be seen from the table that the parameters nhp and Gf are situated in the lower part of the table while the parameter TT occupies the first place.127 0.141 0.35 0.17 0. . A nomenclature of possible diagnoses d1 . 4. namely.q . Dq . a flow parameter ΔA and an efficiency parameter Δη . dq corresponds to the accepted classification (16).. Θ0 ) Yi (U . During the calculations a variable fault severity is determined by a uniform distribution and errors are generated according to a normal distribution.Gas Turbine Condition Monitoring and Diagnostics 135 Concluding section 3. i = 1. In the pattern recognition theory. a fault classification necessary to apply pattern recognition methods is usually constructed in a deviation space using nonlinear or linear static models.. To make a diagnosis d. j = 1. the normalized deviations induced by a change ΔΘ in fault parameters can be written as Zi = Yi (U . In expression (15) amplitudes of random errors ε i are equal to one for all monitored variables Yi . It is also assumed that each class corresponds to one engine component and is described by the correction factors of this component. Diagnosis by pattern recognition methods 4. the learning set is used. we would like to note that the considered here stage of data validation and computing deviations has received increased attention because this preliminary stage has utmost importance for subsequent general stages of a total diagnostic analysis. a method-dependent criterion R j = R( Z * . To determine the functions R j = R(Z* . A considerable part of these studies are based on the pattern recognition theory. for the purposes of engine diagnostics this variety has to be broken down into a limited number of classes. Two types of classes are simulated: a single fault class and a multiple one. Hence. The whole classification is a composition of these samples Zl called a learning set. it is often supposed that an object state D can belong only to one of q preset classes D1 . Dj ) . detailed diagnosis or fault identifications can be considered as a principal stage and it is addressed in the most of studies in the area of gas turbine diagnostics. Θ0 + Δ Θ) − Yi (U ... That is why. models are used in gas turbine diagnostics to describe engine performance degradation and faults and the deviations are employed to reveal the degradation influence. (15) where coefficients aYi are employed to normalize deviations.1 Technical approach to diagnosis at steady states As mentioned in sections 2 and 3. The deviation vector Z * is considered as a pattern to be recognized and a fault classification is presented as a set of such patterns. (16) We accept this hypothesis for a gas turbine fault classification. Each class is given by a representative sample of the deviation vectors Z * computed according to expression (15).. Such normalization simplifies fault class description and enhances diagnosis reliability. The single fault class is formed by changing one fault parameter. d2 . D2 . After calculating all values R j . Engine faults vary considerably.. Employing the nonlinear model. m .. Among these stages. Θ0 )aYi → → → → → → → + ε i . D j ) is introduced as a measure of membership of a current pattern Z * to class Dj. The multiple fault class has two independently changed parameters for the same component. a decision rule . These elements make up probabilities of false diagnosis Pe j = 1 − Pj and Pe = 1 − P . 2007). and a power turbine. Rq ) (17) is applied. in particular. is created in the same way as the set Zl ..136 Gas Turbines d = dl if Rl = max( R1 . Following the presented approach. Eleven full and partload steady states are set by the following speeds: 10700. The only difference is that other series of random numbers is generated to simulate fault severity and errors in the deviations. that is why this function can be determined only for a simplified class description. we can compute probabilities Pdlj = P( dl / D j ) and compose a known confusion matrix Pd. The necessary set Zv . which are simulated by nine fault parameters. Every pattern in the validation set pertains to a known class. with measurements at these points. called a validation set. The first technique is based on the Bayesian approach (Duda et al. The resulting diagnosis reliability indices – the probabilities of false diagnosis Pe j and Pe for the multiple faults – are placed in Table 2. comparing this class D j with the diagnosis dl . The third technique applies the neural networks. formation of a diagnostic algorithm. a gas generator turbine. a combustion chamber. 9800. in which each fault class Dj should be described by its probability density function f (Z * / D j ) and a posteriori probability P(D j / Z * ) is employed as a decision criterion. Thus. some studies have been conducted for the GT1 chosen as a test case. The single type fault classification consists of nine classes.. a generalized deviation vector is computed. The criterion R j for this technique is an inverse averaged distance between an actual pattern and all patterns of a fault class D j . A transient interval is divided into T time points and. No diagonal elements help to identify the causes of bad class distinguishability. Difficulty of this method is related with the function f (Z * / D j ) as far as density function assessment is a principal problem of mathematical statistics. the described approach to gas turbine diagnosis under stationary conditions includes the fault classification stages. and estimation of diagnosis reliability indices.. It is a pattern to be recognized in diagnosis under transient conditions. 2001). one more set is required. 9700 rpm. 4.2 Comparison of recognition techniques Three recognition techniques that present different approaches in a recognition theory have been chosen for diagnosing. Six simulated gas path variables correspond to a standard measurement system of the GT1. The first conducted study (Loboda & Yepifanov. The multiple type classification comprises four items corresponding to four main components: an axial air compressor. 2006) compares different recognition tools. …. The given indices demonstrate that . a multilayer perception. That is why. Mean number of these elements – scalar P – characterizes total engine diagnosability. Its diagonal elements Pdll form a vector P of true diagnosis probabilities that are indices of classes’ distinguishability. R2 . The second technique operates with the Euclidian distance to recognize gas turbine fault classes. In these studies steady state operation is determined in the thermodynamic model by a fixed gas generator speed and standard ambient condition. The learning and validation sets include 1000 patterns for each class that are sufficient to ensure the necessary computational precision.. To verify a diagnostic algorithm determined with the help of the learning set... With several small corrections this approach is also applicable for diagnosis at transients (Loboda et al. 10600. In this table." means the probabilities for the conventional classification averaged over all steady states. 2007) that drastically simplifies practical realization of diagnostic algorithms.117 0. It proposes and verifies the idea of the generalized fault classification (Loboda. Yepifanov et al. Table 3 contains the results for the single class type. The same problem arises for diagnosis at transients but existing works do not answer how to overcome it. the same steady states. Loboda & Feldshteyn. neural networks can be recommended for the use in real condition monitoring systems. It can be noted that differences of the probabilities Pe between the considered classifications are small for the both class types.104 0.109 0. Therefore we intended to draw up the classification that would be independent from operational conditions.051 0. Additionally.1 implies that a laborious procedure of fault classification formation is repeated for every new operating condition. It will be difficult to realise this approach in practice because an engine frequently changes its operating mode.127 0.1790 3 0. it has been found out that the class presentation in the diagnostic space Z is not strongly dependent on a mode change. because the latter in its turn is known as the best recognition technique if we use the criterion of a correct decision probability.216 0.3 Generalized fault classification The approach presented in subsection 4. In this way. neural networks do not need the simplifications of the fault class description required for Bayesian approach.072 0. But how significant are these losses? Numeric experiments with traditional and new classifications helped to quantify such losses. a region occupied by any class is more diffused that induces greater class intersection. the row "Conv.060 0. It is important that neural networks are not inferior in diagnosis accuracy to the Bayesian approach. False diagnosis probabilities (multiple type classification) 4. Neural networks will also be used in the next study. Such generalized classification was successively applied to diagnose at each steady state.. The . The calculations for single faults have confirmed this conclusion. Indices d1 → 1 0.237 0. This classification has been created by incorporating patterns from all 11 steady states into each class of the reference and testing sets.1256 d2 d3 d4 Methods 2 0. In the classification. The row "Gen. 2007. the classification comparison was drawn for both single and multiple class types." contains the probabilities for the generalized classification created for. Diagnosing the considered gas turbine (GT1) at different operating modes.214 0.Gas Turbine Condition Monitoring and Diagnostics 137 probabilities of erroneous diagnosis by methods 1 and 3 are approximately equal and significantly lower than the corresponding probabilities of method 2.373 0. To ensure firm conclusions. and applied at. which in its turn leads to losses in the diagnosis reliability.051 0.1293 Pe Pe Table 2. 146 0.148 Δηpt 0. This still holds true when the classification is used at the operating points different from the points of classification formation. the results have shown that the generalized classification practically does not reduce the diagnosis accuracy level. Therefore. 2007) the examination is conducted at 16 transients with different transient profiles and ambient temperatures.5%. In (Loboda.132 0.". Consequently. Yepifanov et al. The losses are estimated at the level of 2% and it is shown that they could be lower in practice. Classification Conv. power turbine. In this way.161 Δηcc 0. Pe ΔAc 0.266 0.166 0. So the diagnosis reliability losses resulting from the classification generalization are insignificant. 2007). The next study briefly described below also deals with networks-based diagnosis under variable operating conditions. the previous analysis was also carried out for real operational conditions. 4. the generalized classification can be applied not only to the steady state points used for its creation but also to any other points. Yepifanov et al. More cases of transient operation are considered in (Loboda & Feldshteyn.275 ΔAhpt 0.269 ΔApt 0. by about 0. In both cases. the suggested classification drastically simplifies the gas turbine diagnosis because it is formed once and used later without changes. Gen. So. Two sets of 25 operating points were made up from a six-month database of gas turbine performance registration at different operational field conditions.172 0. The diagnosis at transient operation (Ogaji et al. On the other hand. ensure higher accuracy when compared with conventional one-point (one-mode) methods. The results show (Loboda.1827 0. which group the data registered at different operating points in order to make a single diagnosis.190 Δσcc 0. and input device) For additional verification of the generalized classification.156 Δηc 0.5%. The resulting accuracy losses due to the classification use did not exceed 3.168 0.138 Gas Turbines mean probability Pe also rises just a little. high pressure turbine. The principle of a generalized classification was also examined for transient operations.4 Multipoint diagnosis Although some works deal with the influence of operating conditions on the diagnostic process (Kamboukos & Mathioudakis..131 Δηhpt 0. the diagnostic technique based on the generalized fault classification can be successfully implemented in gas turbine health monitoring systems. the proposed classification principle was verified separately for steady states and transients. no full-length analyses are yet available.180 → Pe 0. However. the data from different operating points (modes) are grouped to set only a single diagnosis.1883 Table 3..154 0.174 0.184 Δσin 0. It is known that multipoint methods. Diagnosis errors for single faults (indices of fault parameters ΔA and Δη mean compressor. combustion chamber. questions arise as to how significant this effect is and what its causes are. 2007) that differences between two classifications are small and can be considered as random calculation errors. In contrast to the previous study. The points of each set correspond to the maximally different conditions. 2003) . 2006). the proposed classification does not cause additional accuracy losses.265 0. Such multipoint diagnosis promises considerable accuracy enhancement. in the row "Gen.. We complete here the descriptions of the studies in the area of diagnosis (fault identification) based on pattern recognition. the averaging effect is responsible for the whole growth. To form a new classification necessary for monitoring. 2007) for the GT1 and an aircraft engine. The investigation to answer the questions has been conducted in (Loboda. 5. DM12. called GT3. The following conclusions were drawn.Gas Turbine Condition Monitoring and Diagnostics 139 poses the similar questions. A totality of subclasses DM11. DM1q (17) . although they are not well distinguishable against a background of random measurement and registration errors. The diagnosis at transients may cause further accuracy growth of this type. …. created for the purpose of diagnosis and presented by the learning set. To make one diagnosis. the main effect of the data joining consists in an averaging of the input data and smoothing of the random measurement errors. they give new information for the fault description and produce an additional accuracy growth for the multipoint option. In the next section it will be shown how to extend the described approach on the problem of gas turbine monitoring (fault detection). The paper (Loboda et al. It corresponds to a decrease in the diagnosis errors by 2-5 times. Hence. corresponds to a hypothetical fleet of engines with different faults of variable severity. Classification (16). Integrated monitoring and diagnosis Detection algorithms deal with two classes. It is responsible for the main part of the total accuracy growth. This part depends on the class type but in any case it is essentially smaller than the principal part. In multidimensional space of the deviations they are divided by a healthy class boundary (internal boundary). faulty class boundary (external boundary) that means an engine failure or unacceptable maintenance costs. First. 2008) thoroughly investigates such approach considering monitoring and diagnosis as one integrated process. the generalized classification has a certain advantage as compared to the conventional one-point diagnosis. this technique joins data from successive measurement sections of one transient and in this regard looks like multipoint diagnosis. Below we only give a brief approach description and the most important observations made. The healthy class implies that small deviations due to usual engine performance degradation can certainly take place. There is an intersection between the patterns Z * of these subclasses because of the errors ε in patterns. patterns of the existing learning set can be used for a new classification but the classes should be reconstructed. it would be interesting to find out how much these two approaches differ in accuracy.. From a theoretical and practical standpoint. if the variations are considerable (GT3). Under these conditions. a total diagnosis accuracy growth due to switching to the multipoint diagnosis and data joining from different steady states is significant. the distributions of faults. namely. Second. However.. If variations in fault description at different operating points are slight as for the GT1. Feldshteyn et al. Each former class Dj is divided into two subclasses DM1j and DM2j by the healthy class boundary. we suppose that the engine fleet. a class of healthy engines and a class of faulty engines. The faulty class requires one more boundary. Third. and their severities are the same. it will be limited and the averaging effect will be a principal part of the total accuracy growth relative to the one-point diagnosis. lines OD1. …. DM1q compose a healthy engine class M1. can reduce monitoring errors. the influence of the boundary on the monitoring and diagnosis accuracy was also investigated. First. The second approach maintained in gas turbine diagnostics and based on system identification techniques can overcome these difficulties. which is different from the boundary. DM2q make up a faulty engine class M2. it was demonstrated that a geometrical criterion. DM22. and ODq are trajectories of fault severity growth for the corresponding single classes. DM12. can provide the same results and thus can also be used in real monitoring systems. A point “O” means a baseline engine. The former and the new classifications are presented here in the space of deviations Z1 and Z2. (19) It is clear that the patterns of these two classes are intersected. while the subclasses DM21. Z2 … Dq DM2q DM2 j DM22 DM21 Dj j … D2 M2 M1 DM1q DM1 j DM12 DM11 D1 Z1 R=1 O B1 B2 Fig. ….140 Gas Turbines constitutes the classification of incipient faults for the diagnosis of healthy engines. DM2q (18) form the classification of developed faults for the diagnosis of faulty engines. resulting in α. The diagnoses made are limited by a rigid classification and fault severity is not estimated. which is much simpler in application than neural networks. Third. M2. the classification for monitoring takes the form of M1. Second. Thus. Schematic class representation for integrated monitoring and diagnosis With these three classifications. OD2. the recognition of incipient faults was found to be possible and advisable before a gas turbine is recognized as faulty by fault detection algorithms. . it has been shown that the introduction of an additional threshold. DM22. Figure 10 provides a geometrical interpretation of the preceding explanations. The pattern recognition-based approach considered in this section is not however without its limitations. To perform the monitoring. …. Fourth. while subclasses DM21. 10.and β-errors. …. monitoring accuracy and diagnosis accuracy were estimated separately for healthy and faulty classes and some useful results were obtained. closed lines B1 and B2 present boundaries of a healthy class M1 (indicated in green) and faulty class M2 (indicated in yellow). the subclasses DM11. 3. Furthermore. Like the polynomial model of a degraded engine described in section 3. Two purposes are achieved by such model identification. The application of the proposed procedure on real data has justified that the regularization of the estimations can enhance their diagnostic value. Other computational scheme is maintained in (Loboda. Next diagnostic development of the gas turbine identification is presented in (Loboda.02-0. or hybrid. successive independent estimation are computed and analyzed in time to get more accurate results. with data recorded over a prolonged period. 2007). (2) or (4). If we put the time variable equal to zero. 2005). Independent estimations are obtained by a special inverse procedure. this model can be easily converted into a baseline model of a high quality. 2007). The estimates contain information on the current technical state of each engine component therefore further diagnostic actions will be simple. every Kalman filter estimation depends on previous ones. for example (Volponi et al.. extended. Θ ) . the model will be transformed into a good baseline function for diagnostic algorithms. see. Moreover. the regularization shifts mean values of the estimations and should be applied carefully.. basic.Gas Turbine Condition Monitoring and Diagnostics 141 6. the values 0. However. Then. the Kalman filter. time variable. In the case of model (1) this minimization problem can be written as Θ = arg min Y * − Y (U . In the conditions of fulfilled calculations. the diagnosis will not be constrained by a limited number of determined beforehand classes. The obtained model taking into account variable gas path deterioration can be successfully used in gas turbine diagnostics and prognostics. Moreover. can result in considerable estimation errors. Among system identification methods applied to gas turbine diagnostics. this method uses a linear model that. a regularizing identification procedure is proposed and verified on simulated and real data in (Loboda et al. 2005). and can be identified on registered data of great volume. The idea is proposed to develop on the basis of the thermodynamic model a new model that takes gradual engine performance degradation in consideration. 2003). These ˆ techniques compute estimates Θ as a result of distance minimization between simulated and measured gas path variables. The idea is verified on maintenance data of the GT1. such a model has an additional argument. On the other hand.03 of the regularization parameter were recommended. The first purpose consists in creating the model of a gradually degraded engine while the second is to have a baseline function of high accuracy. Diagnosis by system identification methods This approach is based on the identification techniques of the models (1). Such a model can be widely used in monitoring systems as well. That is why abrupt faults are detected with a delay. The testing on simulated data has shown that the regularization of the estimated state parameters makes the identification procedure more stable and reduces an estimation scatter. ∧ → → → → → (20) It is an inverse problem while a direct problem is to compute Y with use of known Θ . Comparison of the modified identification procedure with the original one has shown that the proposed identification mode has better properties. . as shown in (Kamboukos & Mathioudakis. is mostly used. Following this scheme. Wiley-Interscience. and Mathioudakis. E. Multipoint non-linear method for enhanced component and sensor malfunction diagnosis. Texas. The chapter contains the basis of gas turbine monitoring and a brief overview of the applied mathematical techniques as well as provides new solutions for diagnostic problems. ASME Paper GT2009-59364 Haykin. D. in particular. fault identification. Journal of Engineering for Gas Turbines and Power. (2001). Different modes to improve a baseline model for computing the deviations are also proposed and justified.. The chapter pays special attention to a preliminary stage of data validation and computing deviations because the success of all subsequent diagnostic stages of fault detection. and Stork. New York Kamboukos. the chapter considers monitoring and diagnostic stages as one united process. pp. Hart. Many improvements are proposed. Different condition monitoring models for gas turbines by means of artificial neural networks. P. To enhance the quality. However. regularized nonlinear model identification procedure. and model of a degraded engine.G. Pike. 2001. Orlando. Ph. and confirmed for fault diagnosis by pattern recognition and system identification methods. Conclusions In this chapter. S. Neural Networks. June 8-12. Proceedings of IGTI/ASME Turbo Expo 2009.. September 17-20.. We hope that the observations made in this chapter and the recommendations drawn will help to design and rapidly tailor new gas turbine health monitoring systems. (2009). generalized fault classification. USA. Houston Duda. 9р. (2001).E.2331. Proceedings of the Thirtieth Turbomachinery Symposium.Texas A&M University. No.49-56 Kamboukos. (2005). 7. M. we tried to introduce the reader into the area of engine health monitoring. 1.. 11p. Pattern Classification. and prognostics strongly depends on deviation quality. In order to draw sound conclusions. which needs to be continued. 2002).142 Gas Turbines Another novel way to get more diagnostic information from the estimations is to identify a gas turbine at transients as shown in (Loboda & Hernandez Gonzalez. reduces monitoring errors. 8. P. (1994). this paper is only the first study. K. Spain. the cases of abnormal sensor data are examined and error sources are identified. and Mathioudakis K. Assadi. Florida. May 8-11 . A. USA. the presented studies were conducted with the use of extended field data and different models of three different gas turbines. On the basis of pattern recognition. Ph. New York Fast. Vol. R. Proceedings of IGTI/ASME Turbo Expo 2006. Comparison of linear and non-linear gas turbine performance diagnostics. (2006). It is shown that the introduction of an additional threshold. Macmillan College Publishing Company. which is different from the boundary between healthy and faulty classes.127. investigated. and Breuhaus. Barcelona. pp.O. M. Innovative gas turbine performance diagnostics and hot parts life assessment techniques. References Benvenuti. S. ASME Paper No. 3-4. (2007). and Santiago. and Feldshteyn. Houston . S. ASME Paper No. No. pp. A generalized fault classification for gas turbine diagnostics on steady states and transients. (2010). Zelenskiy. Vol. A universal fault classification for gas turbine diagnosis under variable operating conditions. 12p. S. International Journal of Turbo & Jet Engines. C. 4. Aerospace Technics and Technology. Vol. Journal of Engineering for Gas Turbines and Power. 2001.R. (2002). 6p. 9p. Berlin. C. November 14-18. Verification of a gas turbine model regularizing identification procedure on simulated and real data. I. GT2008-51449 Loboda. No. Germany. I. (2005). E. 8p. GT2010-23075. pp. Yepifanov. UK. (2001). Yepifanov. and Hernandez Gonzalez. and Feldshteyn. I. I. Ya. (2007). ESIME-IPN. Vol.. рp. Deviation problem in gas turbine health monitoring. 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IEA. 2. the electrical current is generated at high frequency and is then converted to the grid frequency value (50 or 60 Hz) by power electronics.7 Micro Gas Turbines 1Dipartimento di Energetica – Università Politecnica delle Marche 2Università degli Studi e-Campus Italy Flavio Caresana1. 2007). Introduction Conventional gas turbines (GTs) range from a size of one or a few MWe to more than 350 MWe (GTW. In the future distributed energy systems based on small local power plants are likely to spread. As a consequence of the high rotational speed. 2002). which also serves as the starting motor. These benefits explain the increasing interest in smallsize generation systems. Their advantages as distributed energy systems lie in their low environmental impact in terms of pollutants and in their competitive operation and maintenance (O&M) costs. have appeared on the market. In particular the low gas mass flow rate is reflected in machine size and rotational speed: the smaller the former. often in combined cycle plants. Recently. mainly in (i) the type of turbomachines used. 2005. MGTs are different from large GTs and cannot therefore be considered merely as their smaller versions.. to achieve greater compactness and low manufacturing costs. MGTs commonly use high-revving. In fact unlike GTs. (ii) the presence of a regenerator.. defined as micro gas turbines (MGTs). The technology of Micro Gas Turbines The small power size of MGTs entails implications that affect the whole structure. gas turbines < 1 MWe. while the larger ones are usually installed in large-scale electrical power plants. 2009). and (iii) the high rotational speed. 2005. MGTs appear to be particularly well suited for service sector. and make thermal energy recovery profitable both in energy-related and in economic terms (Papermans et al. Zogg et al. single-stage radial turbomachines rather than multi-stage axial ones. Gabriele Comodi1. Those at the small end of the range are commonly used in industrial applications. The turbocompressor and turbine are usually fitted on the same shaft as the electrical generator.. since they lie close to the final users. which is independent of grid frequency. Leonardo Pelagalli1 and Sandro Vagni2 1. and are typically located far away from the consuming region. Single-stage radial machines afford limited compression ratios and need a regenerative cycle to attain satisfactory electrical efficiency. for mechanical or onsite electrical power production. MGTs therefore differ significantly from GTs. they reduce electrical transport losses. household and small industrial applications (Macchi et al. . and is conveyed from the regenerator (3) to the combustion chamber. the layout and corresponding thermodynamic cycle of a typical cogeneration MGT. Figures 1 and 2 show. MGT regenerative Brayton-Joule cycle The ambient air (1.2 4.6 3. Fuel 4 CC 3 R PE EG GC GT 5 Electricity 2 PE EG GC GT Power Electronics CC Electrical Generator R Gas Compressor BPV Gas Turbine HRB HRB 6 7 Exhausts Water In Water Out BPV Combustion Chamber Regenerator ByPass Valve Heat Recovery Boiler Fig. it then enters the regenerator (2).4 Fig. 1. where it is preheated by the exhausts coming from the turbine.2 5.8 4 6 7 4. where it is used in the . Layout of a typical cogeneration MGT 1000 900 800 700 600 t (°C) 500 400 300 200 100 0 4 3 5 2 1 3.6 4. in both figures) is compressed by the centrifugal compressor. 2.8 s (kJ/(kg K)) 5 5. respectively.4 4.146 Gas Turbines Therefore a regenerator is usually installed between the compressor and the combustion chamber. and (iv) control systems. lubrication oil included. part of the fumes is conveyed directly to the chimney (7) via a bypass valve (BPV). Thermal priority operating mode Thermal priority operation involves complete closure of the MGT bypass valve. 4. Operation modes MGTs can usually operate in two modes: 1. the exhausts can be sent to a heat recovery boiler (HRB). The cooling fluid can be air. with the dual effect of reducing friction and removing heat. The core power unit is fitted with auxiliary systems that include (i) fuel. The function of the electronic control system is to monitor MGT operation through continuous. water.Micro Gas Turbines 147 combustion process to achieve the design turbine inlet temperature (4). The hot gases then expand through the turbine (5) and enter the regenerator. these findings can be extended to most MGTs. Given their fairly high temperature at the power unit exit (6). a. With due caution. This is not an energy efficiency-optimized operating mode. (ii) lubrication. Cogeneration (combined production of electrical and thermal energy): the MGT produces the electrical and thermal power required by the user. The cooling system keeps the operational temperatures of the different components. 2. (iii) cooling. The data presented below have been obtained from theoretical studies and experimental testing of a specific machine. so that all the exhaust gases from the regenerator pass through the HRB for thermal power recovery. Electrical priority operating mode In this operating mode the MGT produces the electrical power set by the user. while heat production is regulated by the BPV installed before the HRB. The fuel feeding system compresses the fuel to the required injection pressure and regulates its flow to the combustion chamber according to the current operating condition. b. The main performance parameters of an MGT are: . 2002). Non-cogeneration (electricity production only): the MGT provides the electrical power required by the user and all the available thermal power is discharged to the flue. When the thermal power demand is lower than the power that can be recovered from the exhausts. 3. where they are used to heat water. Performance and emissions The considerations made so far apply to most MGTs. In this section. The lubrication system delivers oil to the rolling components. MGTs operating in cogeneration mode can usually be set to work with electrical or with thermal power priority. the performance and emissions of a real MGT-based plant are reported and some criticalities connected to MGT behaviour highlighted. a Turbec T100 PH (Turbec. Thermal power production is regulated by setting the electrical power. real time checking of its main operational parameters. before being discharged to the flue (7). because in conditions of high electrical and low thermal power demand a considerable amount of the recoverable heat is discharged to the flue. which the authors have been using for their research work for several years (Caresana et al. This mode maximizes MGT efficiency in all operating conditions. in the design ranges. or both. 2006).. In this configuration combined heat and power (CHP) production increases fuel energy conversion efficiency. The tests were conducted at a constant water flow rate of 2 l/s entering the HRB at a temperature of 50 °C. Since electrical power is the main final output. we have represented the dependence of the other performance parameters on Pel (Figures 3-7). respectively. . 1989). defined as: Gas Turbines η el = • thermal efficiency ηth . defined as: Pel m f LHV (1) ηth = • total efficiency ηtot . electrical efficiency η el .e. defined as: Pth m f LHV (2) ηtot = Pel + Pth = η el + ηth m f LHV (3) where m f and LHV are the mass flow rate and the Lower Heating Value of the fuel. with a maximum slightly > 29 % around 80 kWe. for different degrees of BPV opening.) equal to 15 °C and 60 % respectively (ISO. Electrical efficiency Figure 3 plots the trend of the electrical efficiency. the experimental data refer to ISO ambient conditions. respectively. calculated as the ratio between the thermal power recovered and that which can be recovered at the nominal power. thermal power Pth . 3. i.148 • • • electrical power Pel . Electrical efficiency (%) 32 30 28 26 24 22 20 18 30 40 50 60 70 80 90 100 110 Electrical power (kW) Fig. Unless specified otherwise. which is consistently high from the nominal power down to a partial load of about 70 %.H. temperature and relative humidity (R. Figures 4 and 5 report the thermal power and total efficiency data. The NOX concentration is very low in all working conditions. greater BPV opening entailed a progressive reduction in the thermal power recovered. If this thermal power (about 25 kW at full load) is usefully recovered. Thermal power for different degrees of BPV opening 80 70 Total efficiency (%) 60 50 40 30 20 10 0 30 40 50 60 70 80 Electrical power (kW) Fig. 4. respectively. as shown in Figure 5. otherwise total and electrical efficiencies necessarily coincide. This confirms that the thermal priority cogeneration mode maximizes fuel energy conversion efficiency. CO concentrations in the exhausts are low from 70 % to 100 % of the load. 5. 0% 60 % 88 % 100 % 90 100 110 . even with a completely open BPV. and consequently reduced total efficiency. total efficiency remains greater than electrical efficiency. Figure 4 shows that a small part of the discharged thermal power is however transferred from the exhausts to the water.Micro Gas Turbines 149 180 160 140 120 100 80 60 40 20 0 30 40 Thermal power (kW) 0% 60 % 88 % 100 % 50 60 70 80 90 100 110 Electrical power (kW) Fig. but they rise steeply with lower loads. Figures 6 and 7 show the level of pollutants CO and NOX. Efficiencies for different degrees of BPV opening As expected. 150 1800 1600 1400 1200 1000 800 600 400 200 0 30 40 50 60 70 80 90 100 110 Electrical power (kW) Gas Turbines Fig. 6. Electrical performance vs ambient temperature Electrical efficiency (%) . 7. CO concentration @ 15 % O2 7 6 NOx (ppm v ) 5 4 3 2 1 0 30 40 50 60 70 80 90 100 110 Electrical power (kW) Fig. 8. NOX concentration @ 15 % O2 130 110 Pel (kW) 90 70 50 -25 -15 -5 5 15 25 35 Ambient temperature (°C) 34 32 30 28 26 CO (ppmv ) Fig. The most commonly used index is the Primary Energy Saving (PES) index which.2 Influence of heat recovery The performance of a cogeneration system can be evaluated by comparison with the separate production of heat and electricity. A parallel decrease in electrical efficiency can also be noted. to avoid overworking the machine.1 Influence of ambient parameters The performance of MGTs. In the T100 PH machine. electrical power generation at temperatures < 0 °C is limited electronically. 2004): PES = 1 − 1 η el _ ref η el + ηth _ ref η th (4) where: η el and η th are the electrical and thermal efficiencies of the cogeneration system • averaged over a given period. 9. as the name suggests. 4.1 PES = 0. Figure 8 shows the values of nominal electrical power and efficiency as a function of the ambient temperature. are strongly affected by ambient conditions.2 Total efficiency = 1 .Micro Gas Turbines 151 4. A positive value of the index means that the primary energy consumption of the CHP system is lower compared with separate production over the time period considered. The PES index is calculated as (European Parliament. particularly temperature. and • η el _ ref and ηth _ ref are the reference values of efficiency for separate production of electrical and thermal energy. quantifies the primary energy savings offered by a CHP plant compared with (conventional) separate production of electrical and thermal energy. PES for different degrees of BPV opening 0% 60 % 88 % 100 % PES = 0 PES = 0. Figure 9 shows the PES index of a Turbec T100 PH in different operating conditions for 100 Thermal efficiency (%) 80 60 40 20 0 0 20 40 60 80 100 Electrical efficiency (%) Fig. like those of GTs. The decline observed at higher temperatures is explained by the lower air density and consequently lower mass flow rate through the power unit. In fact. The air intake system of the MGT studied consists of a single duct carrying the working air and the cooling air. The refrigerating engine and the condenser fans are electrically driven by means of inverters. to enhance MGT performance.) that are much more severe than those that can be achieved with any cooling system. i. only the air processed by the compressor influences performance.1 Inlet Air Cooling (IAC) The simplest way to limit the power reduction consequent to rising ambient temperature is to cool the air entering the compressor. reciprocating engines. This confirms that thermal priority operation (0 % BPV opening) is the mode maximizing fuel savings and consequently that it is preferable to the electrical priority mode. in order to cool only the working air. This can be achieved with minimum changes to the MGT cabinet and by mounting a cooling system in the working air inlet duct. Their main advantages. Bottoming organic Rankine cycles. 3. whose evaporator is housed directly in the working air intake duct. which both enter a single ambient inside the cabinet. • fogging IAC system. Ancona. Clearly. For the MGT model studied ice formation in the air flow and on the walls. do not seem to offset these drawbacks. Micro STIG. Enhancing performances As noted above. We used a test bed to evaluate two different IAC techniques: • direct expansion IAC system. . Italy. 5. 2. is excluded by the manufacturer. respectively. The tests were conducted in the summer in the ambient condition of an Adriatic seaside town in central Italy. In the following paragraphs we describe the research work being conducted by the Systems for Energy and the Environment team of Dipartimento di Energetica. and lower electrical power production at rising ambient temperatures.152 Gas Turbines different degrees of BPV opening. Hence the need for separating the two flows. From here part of the air is sucked in by the compressor. external ambient conditions and refrigerating engine power permitting. The system uses R507A as the refrigerating fluid and is designed to keep the inlet air temperature at the value set by the user. 5. 100 % R. Trigeneration.e. while the remaining air flow is conveyed to the cooling system via an external fan.H. 4. focusing on: 1. Direct expansion IAC system This system consists of a refrigerating engine. even minor opening of the BPV adversely affects the index. major limitations to the further spread of MGTs are their lower electrical efficiency compared with their main competitors. a common risk in GTs. We employed the same MGT model that was used to obtain the experimental performance and emissions data. Università Politecnica delle Marche. low emissions and competitive O&M costs. Inlet Air Cooling (IAC). to improve efficiency. calculated considering values of 40 % and 90 % of η el _ ref and ηth _ ref . who states extreme working condition (-25 °C air temperature. In fact. It is worth noting that heat recovery is crucial to achieve a positive PES. R.H. and corresponding IAC temperature over 200 time steps (about 15 min). respectively. t 20 15 10 5 0 Fig.H. 70 65 60 55 50 0 50 100 150 Time steps 200 Ambient R. (%) Electrical efficiency (%) Electrical efficiency according to ambient temperature (%) Ambient temperature (°C) IAC temperature (°C) ηel. However.. with the machine working at maximum load. Effects of the direct expansion IAC system on inlet air and MGT electrical power production 35 30 25 85 80 75 R. Figures 10 and 11 show the electrical power and efficiency. the net electrical power. was greater than the design R.H. 10. in relation to ambient temperature. 11. (50 %). Since the R. due to the strong influence of the refrigerating engine performance: the lower its coefficient of . the minimum IAC temperature that could be achieved was slightly > 15 °C (about 17 °C).H. (%) Ambient temperature (°C) IAC temperature (°C) Fig.H. 1989) was set for all the tests. from about 80 kW (without IAC) to around 95 kW.H.Micro Gas Turbines 153 although an inlet air cooled temperature of 15 °C (ISO. reached only 84 kW. it was not reached consistently. 100 80 60 40 20 0 0 50 100 150 Time steps 200 Gross electrical power (kW) Net electrical power (kW) Electrical power according to ambient temperature (kW) Ambient R. Effects of the direct expansion IAC system on inlet air and MGT electrical efficiency The IAC temperature induced a significant increase in gross electrical power production. which is the crucial output. As an example. such as air conditioning of large spaces (e.H.g. The power increase notwithstanding. the final cool air temperature cannot be preset. (%) Fig. Fogging IAC system This system cools the inlet working air via adiabatic saturation (Chaker et al. ambient conditions permitting. Expansion techniques would be interesting if the refrigerating engine were also used for other purposes. To sum up. cinemas. The COP thus emerges as a crucial parameter. they work at partial load most of the time. Figures 12 and 13 show electrical power and efficiency. 2000). but is strongly dependent on ambient conditions: the drier the air. office blocks). by about 1 %. Since air conditioning plants are designed on the warmest local conditions. For this reason. the residual power could therefore be used for IAC. The main components of the apparatus are nozzles (4 in our test bed) and a high-pressure pump. electrical power production increases from about 84 kW to 88 kW. since the highpressure pump consumes only 550 W. shopping malls. of about 100 %. Demineralized water is pumped at a pressure of 70 bar to the nozzles. cheaper plant. and is then nebulized as droplets whose diameter is usually < 20 µm (Chaker et al. since besides enhancing efficiency it involves a much simpler and. the higher its consumption and the lower the net electrical power of the MGT. both IAC techniques were effective in limiting the electrical power reduction consequent to rising ambient temperature. last but not least. Furthermore. Effects of the fogging IAC system on inlet air and MGT electrical power production . 12. the fogging system slightly improves electrical efficiency..H. Thanks to the IAC temperature. over a period of 200 time steps with the machine working at its maximum load.5. the direct expansion IAC system can be used to increase electrical power. here it is very close to the net electrical power. the fogging technique is however preferable. Despite the comparable power gain. since an excessively low COP can entail a net electrical power even lower than the one without IAC. the greater the temperature reduction.H. at an R. the consumption of the refrigerating engine adversely affects the electrical efficiency of the MGT.. The COP measured during these tests was about 2. which is the lowest achievable temperature. housed in the intake duct. respectively.154 Gas Turbines performance (COP). The fogging system thus achieves nearly total adiabatic saturation by cooling the air to wet bulb temperature. In conclusion. 120 100 80 60 40 20 0 0 50 100 150 Time steps 200 Ambient temperature (°C) IAC temperature (°C) Fogging outlet R. 2002). but it does not enhance efficiency. (%) Electrical power (kW) Electrical power according to ambient temperature (kW) Ambient R. but unlike in the direct expansion IAC system. H. 70 65 60 55 50 Electrical efficiency (%) Electrical efficiency according to ambient temperature (%) Ambient temperature (°C) IAC temperature (°C) Ambient R. 13.. producing additional electricity.2 Bottoming organic Rankine cycles The solution proposed here aims to enhance the electrical efficiency of the MGT by recovering the heat lost. t 15 10 5 0 0 50 100 Time steps 150 200 Fig. (%) 35 30 25 20 ηel. 14. Layout of the micro combined plant .H. The vapour generated in the HRVG expands through a turbine that drives an electrical generator. a Heat Recovery Vapour Generator (HRVG). This micro combined configuration consists of an MGT.Micro Gas Turbines 155 85 80 75 R. The MGT exhausts enter the HRVG and are discharged to the environment after heating the bottoming working fluid. since it merely requires replacing the original HRB with an HRVG. This solution minimizes the changes to the standard CHP model. 2008). Ex In 3 Ex Out CC HRVG R EG GC GT EG 4 VT C MTG EG GT R VT P Electrical Generator Gas Turbine Regenerator Vapour Turbine Pump GC CC C HRVG P 1 2 Gas Compressor Combustion Chamber Condenser Heat Recovery Vapour Generator Fig. and a bottoming vapour plant (Figure 14). Effects of the fogging IAC system on inlet air and MGT electrical efficiency 5. This goal can be achieved with a micro combined cycle using bottoming organic Rankine cycles (Caresana et al. • global warming-neutral. organic fluids seem to be more appropriate in micro scale plants. technically suitable organic fluids. 15. In fact. because they will be banned in the European Union. large-size.8 1. 180 160 140 120 t (°C) 100 80 60 40 20 0 0. Compared with steam. • low ozone-depleting. HFCs meeting these criteria include R245ca. by virtue of their significantly narrower density variation through evaporation and expansion.7 1. and hydrochlorofluorocarbons (HCFCs). R245fa.5 1. organic fluids allow both more compact solutions. the last two being mixtures. Therefore the choice necessarily falls on hydrofluorocarbons (HFCs) due to thermo-physical and technical criteria. T-s diagrams of five HFC organic fluids .9 2. • compatible with the plant’s process component materials. • non-explosive. the fluid in question needs to be: • thermally stable in the range of pressures and temperatures involved in the cycles.e. because they have been banned (United Nations. This work does not examine some common.0 1. • non-corrosive.3 1.4 1. from January 1st 2015 (European Parliament. this configuration greatly affects the cogeneration plant’s performance. • non-flammable. R134a.8 0. and simpler layouts.156 Gas Turbines Clearly. Selection of the bottoming cycle working fluid Whereas traditional.6 1. 2000). i. 2000).0 s (kJ/(kg K)) R245ca R245fa R134a R407C R410A Fig. R407C and R410A.9 1. chlorofluorocarbons (CFCs).2 1. Their liquid-vapour curves are reported in a T-s diagram in Figure 15 and their critical properties in Table 1. combined plants commonly use water as the bottoming cycle working fluid. because their thermodynamic properties are better suited to the low temperature of the exhausts leaving the MGT. • non-toxic. since the thermal energy is discharged at the bottoming cycle condenser at very low temperatures.1 1. by virtue of their higher density. In fact. mV .059 R407C 86. pv . Use of a dry fluid prevents droplet condensation in the turbine even without superheating. • vapour cycle maximum temperature. superheating is still a valuable option. since the benefit of removing the superheater must be weighed against the consequent decrease in efficiency. Pt _ rec . setting the exhaust temperature at the HRVG outlet. allows calculation of the thermal power that can be recovered from the exhausts. tEx Out . respectively. and an isoentropic fluid is a fluid having a vertical saturation line (dT/dS= ∞). t3 . (ii) superheated or Hirn type. the bottoming cycles can be defined completely by setting the values of the following parameters: • vapour cycle condensing pressure. R245ca Temperature (°C) Pressure (MPa) 174. Since the exhaust mass flow rate and outlet temperature of the MGT studied are known. as: Pt _ rec = meg ⋅ c p _ eg ⋅ tEx In − tEx Out ( ) (5) where meg and c p _ eg are the exhaust mass flow rate and its specific heat. Steam cycles are commonly superheated. • HRVG pressure. Considering the HRVG as adiabatic. due to thermodynamic efficiency requirements and to the need for limiting droplet condensation during vapour expansion through the turbine. pc . However. where different vapour cycle configurations were tested using the five organic fluids mentioned above. at a suitable evaporating pressure the expanding dry fluid does not enter the liquid-vapour equilibrium zone and condensation does not take place. performed with an in house-developed program.42 3.05 3.06 4.Micro Gas Turbines 157 In particular Figure 15 shows that R245fa and R245ca are “dry fluids”.925 R245fa 154.640 R134a 101. a wet fluid is one having a negative slope (dT/dS<0). which is equal to the increase in enthalpy through the HRVG: qin = h3 − h2 (7) . or (iii) supercritical. is therefore: mV = Pt _ rec qin (6) where qin is the heat received by the organic fluid unit of mass (see fluid states of Figure 14). A dry fluid is one whose vapour saturation curve with reference to a given temperature interval has a positive slope on a T-s diagram (dT/dS>0). In this subsection we present the results of simulations. the organic fluid mass flow rate. Critical points of the five HFCs Bottoming cycles Vapour cycles can be: (i) non-superheated or Rankine type. even starting from the saturated vapour line.903 Table 1.03 4. Furthermore. R407C and R410A are “wet fluids”. and R134a is an almost “isoentropic fluid”.36 4.630 R410A 71. With organic cycles the latter problem is partially addressed by proper selection of the working fluid. tc . of: tc = tcf _ in + Δtcf + τ (8) where. tcf _ in . it examines condensation with water coming from a panel heating system. 16. such as cooling towers. The values of τ and Δtcf are the result of a technical and economic trade-off. the temperature of the water from the cooling tcf _ in (°C) 15 12 15 30 Δtcf (°C) 8 8 8 5 τ (°C) 7 7 7 7 tc (°C) 30 27 30 42 . the assumed values of tcf _ in . In particular. as well as the heat exchanger’s surface and cost. of 60 % are assumed for condensers cooled by ambient air and by water from a cooling tower.H. according to the ambient ISO conditions considered for the gas cycle. it also addresses cooling technologies that reduce the amount of water needed. or that completely obviate the need for it. However.158 Gas Turbines The condensing pressure pc depends closely on the temperature of the cooling fluid at the condenser. Finally. as shown in Figure 16. the lower the condensing temperature and the greater the cycle’s efficiency. which makes the plant a micro combined cogeneration system. The study considers four condensing technologies. of which the water-cooled system is the most appropriate. The condensing technologies considered. The lower these values. τ and the resulting tc and pc are reported in Table 2. Condenser heat exchange diagram Condensing technology Condenser cooled by ambient air Condenser cooled by ambient water Condenser cooled by water from cooling tower Condenser cooled by water from panel heating Table 2. 4 Temperature Organic fluid Cooling fluid 4′ 1 τ Δtcf Thermal power Fig. Δtcf is the temperature increase of the cooling fluid through the condenser and τ is the temperature difference between the condensing organic fluid and the cooling fluid at the outlet. Main parameters of the condensing technologies An air temperature of 15 °C and an R. such as air condensers for use at sites where water is not consistently available. and results in a condensing temperature. Δtcf . if the heat discharged by the vapour cycle is recovered in a panel heating plant. all relevant plant parameters can then be obtained using the set of equations listed in Table 3. Equations used to define the main parameters of the combined plant .Micro Gas Turbines 159 tower is assumed to be 4 °C warmer than the wet bulb temperature of the air. For the water cooled condenser. the ambient water temperature is assumed to be 12 °C. 5-18). which is about 11 °C in ISO conditions. Hirn and supercritical bottoming cycles using this set of equations (eqs. it is considered to require water at 35 °C. Once pc has been calculated. The heat exchange and T-s diagrams of the different cycle configurations examined are reported in Figures 17-22. Finally. minimum vapour quality at the turbine outlet equal to 0. For each condensing pressure. Vapour cycle output heat per unit of mass Vapour cycle expansion work per unit of mass Vapour cycle pumping work per unit of mass Vapour cycle thermodynamic efficiency Vapour cycle electrical power Combined plant electrical power Combined plant electrical efficiency Vapour cycle thermal power output Combined plant thermal efficiency (panel heating system) Combined plant global efficiency (panel heating system) qout = h4 − h1 lturbine = h3 − h4 = ( h3 − h4 is ) ⋅ηturbine lpump = h2 − h1 = h2 is − h1 (9) (10) (11) (12) η pump η= lturbine − lpump qin ⎡ ⎛ lpump Pel _ V = ⎢ lturbine ⋅ηm _ t ⋅η el _ g − ⎜ ⎜ ηm _ p ⋅ η el _ p ⎢ ⎝ ⎣ ( ) ⎞⎤ ⎟ ⎥ ⋅ mv ⋅ η aux (13) ⎟⎥ ⎠⎦ (14) (15) (16) (17) Pel _ CC = Pel + Pel _ V η el _ CC = Pel _ CC m f ⋅ LHV Pth _ CC = mV ⋅ qout ηth _ CC = η g _ CC = Pth _ CC m f ⋅ LHV m f ⋅ LHV Pel _ CC + Pth _ CC (18) Table 3. minimum temperature difference. the optimization process involved identification of the combination of pv and t3 maximizing the efficiency of the combined plant and meeting the following conditions: 1. 2. which then returns to the condenser at 30 °C. The efficiency of the combined plant was then optimized for Rankine. where the indexes refer to the points in Figures 14-22 and the assumed efficiencies are listed in Table 4. of 15 °C between the exhausts and the organic fluid inside the HRVG. τ min .9. 8 4is 2.6 4′ 1. 17. 18.70 0.80 ηm _ t η el _ g η pump ηm _ p η el _ p η aux η aux * The power used by fan coils is assumed to reduce the auxiliary system efficiency of the air-cooled condenser and of the cooling tower Table 4.2 1.4 1. Rankine cycle .0 2′ 3 4 1≈2 1.0 s (kJ/(kg K)) Fig. Rankine cycle heat exchange diagram 200 150 t (°C) 100 50 0 1.98 0.75 0. Efficiency values assumed for the calculations Ex In Temperature Exhausts Organic fluid 3 2′ Ex Out τmin 2 Thermal power Fig.160 Turbine efficiency Turbine mechanical efficiency Electrical generator efficiency Pump efficiency Pump mechanical efficiency Pump motor electrical efficiency Auxiliary system efficiency (water-cooled condenser and panel heating system) * Auxiliary system efficiency (air condenser and cooling tower)* Gas Turbines ηturbine 0.98 0.92 0.97 0.90 0. Supercritical cycle heat exchange diagram .4 1.2 s (kJ/(kg K)) Fig.2 1. 21. 19.8 2. Hirn cycle Ex In Exhausts Organic fluid Temperature 3 τmin Ex Out 2 Thermal power Fig. 20.Micro Gas Turbines 161 Ex In Temperature Exhausts Organic fluid 3 2″ 2′ τmin Ex Out 2 Thermal power Fig.0 2′ 2″ 3 4 4is 1≈2 1. Hirn cycle heat exchange diagram 200 150 t (°C) 100 50 0 1.0 2.6 4′ 1. due to the lower pressure and temperature levels and to the simpler plant configuration. 22. especially. The performances of the latter cycles are slightly better than that of the Rankine cycle.162 Gas Turbines 250 200 t (°C) 3 150 100 50 0 1. thus also maximizing both the power production and the electrical efficiency of the whole micro combined plant. with slightly better results for the former. the supercritical cycle (37 . but they are based on significantly higher values of HRVG pressure and of t3.2 s (kJ/(kg K)) Fig.0 2. The main results of the optimization processes for the ambient water condenser are reported for illustrative purposes in Table 5. Even though these fluids can be employed in Rankine cycles. The Rankine bottoming cycle therefore remains a good option. achieving an electrical efficiency of 36 . where the electrical power produced by the bottoming cycle is plotted as a function of the evaporating pressure and is parameterized with reference to the t3.2 1. . The electrical power that can be achieved based on tc with R245ca supercritical cycles as a function of the evaporating pressure is reported in Figure 24 with reference to the water cooling technology.6 4 4′ 1.37 %. Table 5 shows the organic fluids R245ca and R245fa to be those offering the best performance. The results of the optimization process of the ambient water condenser with R245fa supercritical cycles are shown in Figure 23. These data are also representative of the other condensing technologies. better results are achieved with the Hirn (37 %) and.0 4is 1≈2 1. where the operating data of each cycle configuration and organic fluid are compared.8 2.38 %). the optimization process highlighted that the ambient water condensing technology maximizes the power production of all bottoming cycle configurations with all the organic fluids studied. Supercritical cycle Performance and results As expected. the only difference being the efficiency of the auxiliary system.4 1. compared with the original 30 % of the MGT. For the Hirn cycle the evaporating pressure is clearly lower than the critical one. Only the dry fluids R245 ca and R245 fa are entered for the Rankine cycle. 74 Hirn mv Pel _ V (kW) 26. Condenser cooled by ambient water (tc = 27 °C) t3 = 227.6 Fig. Pel_V as a function of pv and t3 for an R245fa supercritical cycle at tc = 27 °C .728 Table 5.0 22.92 8.74 36.32 Pel _ CC (kW) 123.66 η el _ CC (%) 38.33 (kg/s) 0.598 0.594 0.586 0.1 8.6 8.577 0.91 (kg/s) 0.6 6.31 tv (°C) 148 129 Pel _ V (kW) 23.57 125.71 11.25 8.62 121.1 5.6 21.24 15.43 (kg/s) 0.89 17.34 8.0 25.33 4.33 9.94 114.66 21.10 13.0 °C 189.78 11.15 11.37 23.60 tv (°C) 186 183 180 162 162 η (%) 16.0 3.42 34.6 5.5 °C 202.89 117.13 117.93 η el _ CC (%) 37.0 °C 214.66 Pel _ CC (kW) 126.36 Rankine η (%) 15.37 123.54 9.5 23.1 6.72 3.47 112.66 Pel _ V (kW) 25.47 12.11 16.01 37.1 7.604 0.38 35.5 Pel_V (kW) 24.0 °C 4.13 17.12 36.630 0.94 14.62 21.66 121.68 17.93 Pel _ CC (kW) 125.0 24.5 °C 177.45 2.14 35.63 4.716 mv Working fluid R245ca R245fa R134a R407C R410A pv (MPa) 3.68 117.1 4.601 mv Working fluid R245ca R245fa 26.40 35. 23.0 21.65 tv (°C) 226 226 181 161 160 η (%) 17.57 25.736 0.05 4.702 0.Micro Gas Turbines 163 Supercritical Working fluid R245ca R245fa R134a R407C R410A pv (MPa) 7.38 33.658 0.5 pv (MPa) 2.5 22.5 25.82 8.65 37.6 pv (MPa) 7.51 13.0 23.32 η el _ CC (%) 37. Figures 26 to 28 report examples of the preliminary results obtained with the model. Pel_V as a function of pv and tc for an R245ca supercritical cycle Figure 24 confirms that the lower the condensing pressure. this applies to all the organic fluids studied. the more the electrical power generated.5 6.0 8. the trend of the electrical efficiency as a function of steam pressure and temperature. Each component was defined by a set of equations describing its mass and energy balances and its operating characteristics.0 pv (MPa) 7. In the micro STIG plant layout reported in Figure 25 the original HRB is replaced with a heat recovery steam generator (HRSG). from a theoretical standpoint. 5. .0 5.5 Gas Turbines tc = 27 °C 30 °C 33 °C 36 °C 39 °C 42 °C 5. the most significant of which are the performance curves of the turbomachines.3 Micro STIG The acronym STIG stands for “Steam-Injected Gas” turbines. a technique used to improve the electrical and environmental performance of large-size GTs. Our group has recently addressed the advantages of applying the well-known STIG technique to MGTs.164 27 26 25 Pel_V (kW) 24 23 22 21 4. respectively. due to the steam injected into the combustion chamber zone. The aim was to devise a mathematical model of the micro STIG plant. despite the influence of the high condensing temperature on electrical performances. Nevertheless. Figures 26 and 27 show electrical power and efficiency. The enhanced electrical power production and system efficiency are related to the different composition and quantity of the working fluid mass flowing through the turbine. which produces the steam to be injected into the combustion chamber. In particular. Figure 28 shows. 24.5 Fig.0 6. The model was used to assess the influence of steam mass flow rate on electrical power and efficiency. The steam also involves a reduction in the combustion temperature and therefore of the NOx formed in the exhausts. as a function of the injected steam mass flow rate in fixed thermodynamic conditions (10 bar and 280 °C). for a given flow rate (50 g/s).5 8.5 7. the cogeneration solution with the panel heating system results in increased global efficiency due to heat recovery. Electrical efficiency vs. injected steam mass flow rate 36 Electrical efficiency (%) 35 34 33 32 0 10 20 30 40 Injected steam mass flow rate (g/s) 50 Fig. 26.Micro Gas Turbines 165 CC Steam R EG GC GT HRSG Water EG GT R Electrical Generator Gas Turbine Regenerator GC CC HRSG Gas Compressor Combustion Chamber Heat Recovery Steam Generator Fig. 25. Layout of the STIG cycle-based micro gas turbine Electrical power (kW) 140 130 120 110 0 10 20 30 40 Injected steam mass flow rate (g/s) 50 Fig. injected steam mass flow rate . 27. Electrical power vs. which limits the working mass flow rate. The plant. Electrical efficiency (%) 35 34 33 32 550 500 450 Steam temperature (K) 0. Electrical efficiency vs. there are fewer applications enabling useful heat recovery in the warm season. Once the amount of steam to be injected has been set. Cogeneration systems are characterized by the fact that whereas in the cold season the heat discharged by the MGT can be recovered for heating.0 1. cogeneration applications that include heating do not work continuously. the latter being a direct exhausts model.1 0. . This configuration.6 0. The recent development of absorption chillers allows production of cooling power for air conditioning or other applications. The exhausts can be conveyed to the boiler or to the chiller. is called trigeneration. thermal and cooling power.2. The main components of an actual trigeneration plant. injected steam thermodynamic state We are currently conducting a sensitivity analysis to assess the thermodynamic state and the amount of injected steam that will optimize the performance of the STIG cycle. the higher its temperature and pressure. apart from industrial processes requiring thermal energy throughout the year. 5. the greater the electrical efficiency. consists of a 100 kWe MGT (right) coupled to a heat recovery boiler (centre) and to a 110 kWf absorption chiller (left).9 1. the amount of steam that can be injected is affected on the one hand by the thermal exchange conditions at the HRSG—which limit its production—and on the other by the turbine choke line.8 0.166 Gas Turbines Preliminary simulations showed that the more steam is injected the greater are electrical power and efficiency. where the same plant can simultaneously produce electrical. whose data acquisition apparatus is still being developed. especially in areas with a short winter. is shown in Figure 29.4 Trigeneration The issue of heat recovery has been addressed in paragraph 4.7 Steam pressure (MPa) Fig. designed by our research group for an office block. In fact. 28. Nevertheless. Thanks to Dr. Falconara e bassa valle dell'Esino". The dependence on ambient temperature can be mitigated by using IAC techniques. In contrast. Cogeneration or trigeneration must therefore be viewed as native applications of MGTs. Trigeneration plant 6. Acknowledgements This work was supported by the Italian Environment Ministry and by the Marche Regional Government (Ancona. The former technology is easier to apply. as well as revision of both the control system and the housing. so that cogeneration applications are often not feasible. since it has already been developed for other low-temperature heat recovery applications. since it does not require design changes to the MGT. Two options have been analysed to increase electrical efficiency: organic Rankine cycles and a STIG configuration. since both discharge heat at lower temperature. Conclusions This overview of the state of the art of MGTs has highlighted the critical function of heat recovery in enhancing the energy competitiveness of the technology.Micro Gas Turbines 167 Fig. the fogging system was seen to be preferable under all respects to an ad hoc-designed direct expansion plant. Silvia Modena for the language review. . Both technologies enhance electrical efficiency to the detriment of global efficiency. Furthermore. 7. but merely replacement of the recovery boiler with an organic vapour generator. the technology is already available on the market. 29. the STIG configuration requires complete redesign of the combustion chamber. The main limitations of the MGT technology are the high sensitivity of electrical power production to ambient temperature and electrical efficiency. Italy) within the framework of the project "Ricerche energeticoambientali per l'AERCA di Ancona. in particular. “Gas turbines . C. R. La Microcogenerazione a gas naturale. & Mee III. pp. Haeseldonckx. J. March 2006 Caresana. D12451. Using MGTs for distributed generation. Pepermans G. 787-795. (2005). Polipress ISBN 8873980163 Milano. Proceedings of the ASME Turbo Expo 2002. Mee III. 413-428. Campanari. T. S. United Nations Environment Programme. C.. & Vagni.“Technical description”... S. psychrometrics and fog generation. & D’haeseleer. F. & Brodrick. 207-218. (2008). Volume 4 A. (2002) Inlet fogging of gas turbine engines .pdf. F. Meher-Homji. Micro combined plant with gas turbine and organic cycle. ISBN: 88-89884-02-9. Volume 1. pp. Meher-Homji. ASHRAE Journal. Pelagalli. G.. Trieste.. 49 (4).. ISBN: 978-0-7918-4311-6.Gas Turbine World Handbook 2009 – Volume 27 IEA (2002). benefits and issues. L. pages 429-441. Metodi di Sperimentazione nelle Macchine. Roth. 2002.. G. Turbec AB. Proceedings of the ASME Turbo Expo 2008. & Vagni. M. measurement and testing.. S. Belmans R. Pelagalli. L. Berlin. Amsterdam. ISSN 0301-4215 Turbec (2002).. ISO 2314: 1989. 17 June 2002 United Nations (2000). D. March 2000 Zogg. T. References Caresana. http://www. June 2002 European Parliament (2000). Energy Policy.. Secretariat for The Vienna Convention for the Protection of the Ozone Layer & The Montreal Protocol on Substances that Deplete the Ozone Layer. J. OECD/IEA 2002 ISO (1989).. (2000) Inlet fogging of gas turbine engines Part A: Theory. (2005). B. Proceedings of ASME Turbo Expo 2000. “Montréal Protocol on Substances that Deplete the Ozone Layer as either adjusted and/or amended in London 1990 Copenhagen 1992 Vienna 1995 Montreal 1997 Beijing 1999”. Bowman.org/textbase/nppdf/free/2000/distributed2002. B. Atti della Giornata Nazionale di Studio MIS-MAC IX. May 2008 Chaker. 48-51 (2007). Directive 2004/8/EC of the European Parliament and of the Council of 11 February 2004 on the promotion of cogeneration based on a useful heat demand in the internal energy market and amending Directive 92/42/EEC GTW (2009) . 787–798. Distributed generation in liberalised electricity markets. Comodi. 33 (2005). Comodi. ISSN 0001-2491. Volume 4 A. R. & Silva.iea. P. (2006). .Part B: Fog droplet sizing analysis. pp. nozzle types. Regulation (EC) No 2037/2000 of the European Parliament and of the Council of 29 June 2000 on substances that deplete the ozone layer European Parliament (2004). May 2000 Chaker.Acceptance tests” Macchi E. Driesen J. W. International Energy Agency. (2007). Distributed generation: definition. pp. Banco prova per la verifica delle prestazioni di una microturbina a gas ad uso cogenerativo.168 Gas Turbines 8. Munich.. K.. M. pp. using simulators the operators can learn how to operate the power plant more efficiently during a lowering of the heat rate and the reducing of the power required by the auxiliary equipment.1 millions of clients that represent almost 80 millions of people. According to Hoffman (1995). In general. analysis of diverse situations. The economical and performance results of a power plant. Ma. 2008).248 MW (the CFE produces 38.1. Gerencia de Simulación 2Centro Nacional de Capacitación Ixtapantongo México 1. Particularly.4 billion worth of non-aviation gas turbines produced in 2008. to be one of the most effective and confident ways for training power plant operators. Basically. 1 Some acronyms are written after their name or phrase spelling in Spanish. Jiménez Sánchez1 and Rafael Cruz-Cruz2 1Instituto de Investigaciones Eléctricas. 2004). the Mexican Utility Company) generates. even not full scope simulators are used successfully for operators’ training. the training of their operators. the infrastructure to generate the electric energy is composed by 177 centrals with an installed capacity of 50. distributes and commercialises electric energy for about 27. According to Fray and Divakaruni (1995). in Mexico. due to the training of the operation personnel with a full scope simulator. Yadira Mendoza-Alegría1. About one million of new costumers are annually added. in particular. Jesús Cardoso G. there exists a feedback from the plant’s directors about improvement in speed of response.457 MW). . either working alone or in combined cycle power plants (and 8% produced directly by gas turbines) that offers an important roll in improving power plant efficiency with its corresponding gains in environmental performance (Rice. The use of real time full scope simulators had proven trough the years. $9. management. Roldán-Villasana1. all these improvements lead to a greater reliable installation. are directly related to different strategies like modernisation. The Comisión Federal de Electricidad (CFE1. Although the proportion that corresponds to the training is difficult to be assessed. A full definition of the used acronyms in this chapter is listed in Section 13.6 billion—more than 80 percent—were for electrical generation (Langston. including those based on gas turbines. about 15% of the installed electrical energy (no counting the electricity generated for internal consuming by big enterprises) is based on gas turbine plants (CFE web page). Introduction Of the $11. Victor M. among other operator’s skills.791 MW and the independent producers 11.8 Gas Turbine Power Plant Modelling for Operation Training Edgardo J. control of operational parameters. transmits. and. at least. in the extremes. The new simulator was decided to be constructed in two stages: the gas-turbine part and the steam-heat recovery part. Here. In 2000 the CFE initiated the operation of the Simulator of a Combined Cycle unit (SCC) developed by the IIE based on ProTRAX. A model may be used for different purposes like design.20-1993 Fossil-Fuel Power Plant Simulators Functional Requirements” norm was adopted as a design specification. The model validation was performed comparing the results with another code (Relap). They used Simulink as platform and they claim that the model may be utilised to represent plants with very different characteristics and sizes. analysis. In this chapter the gas-turbine simulator development and characteristics are described. Vieira et al. exploiting and maintenance. deterministic models of industrial processes are considered (ignoring the stochastic and discrete events models). Colonna & van Putten (2007) list various limitations on this software. (2001) to evaluate the influence of small gas turbines in an interconnected electric network. optimisation. because there is no full access to the source programs. the CFE determined to have a new combined cycle simulator using the open architecture of the IIE products. The goal is to reproduce the behaviour of. training. Some gas turbine models have been reported to be used in different applications. Besides. A dynamic mathematical model of a generic cogeneration plant was made by Banetta et al. 2008). All the revised works report to have a gas turbine system like the presented in Figure 1. Kikstra & Verkooijen (2002) present a model based on physical principles (very detailed) for a gas turbine of only one component (helium). showing the first to having better results (Roldán-Villasana & Mendoza-Alegría.170 Gas Turbines The Simulation Department (SD) belongs to the Electrical Research Institute (IIE) and is a group specialised in training simulators that design and implement tools and methodologies to support the simulators development. Nevertheless. A description of the technique to formulate and solve the models is explained below in this chapter. the value of the variables and their dynamics. Thus. To accomplish with the described goal. with the real time modelling approach (for operators’ training) somewhere in the middle. the variables reported in the control station of a gas turbine power plant operator in such a way the operator cannot distinguish between the real plant and the simulator. education.. although the ideal gas assumption was used. etc. a commercial tool to construct simulators. No details are given concerning the independent variables. for example. The approach was a sequential solution with a lumping parameters approach (non-linear dynamic mathematical system based on discrete time). to empirical models like curves fitting. The model was developed to design a control system. 2006). However. this reproduction may be made considering both. . a comparison between the approaches of the IIE and other simulators developer was made. A common approach is to consider the work fluid as an ideal gas. the combustor behaves ideally and no thermodynamic properties are employed. Modelling approaches and previous works There is not a universal method to simulate a process. The approach depends on the use the model will be intended for and the way it is formulated. 2. The models for operation training are not frequently reported in the literature because they belong to companies that provide the training or development simulators services and it is proprietary information (see. In fact there would be a huge task trying to classify the different ways a model may be designed. The modelling techniques may vary from very detailed physical models (governing principles) like differences or finite elements. the “ANSI/ISA S77. An ideal gas model was considered and the gas composition was not included. They validated the model against plant data. The combustion was simulated with a temperature increase of the gas as a function of the mass flow and the fuel high heating value. No information was provided regarding the input variables. temperatures. The combustor was modelled considering a complete combustion like a difference between the enthalpy of formation of the reactants and the combustion products. The goal was to compare the real plant data with those produced by a model that reproduces the plant variables at ideal conditions. The conclusion was that a good model has to reproduce the correct thermodynamic behaviour of the fluid. . Jaber et al. The input data were the ambient conditions and the air cooling system configuration. Compressors and turbines take into account the efficiencies (adjusted with plant results) and the enthalpies of the gases (but no information was provided how the enthalpies are calculated as a function of measured plant data). The combustion was considered perfect and no heat losses were modelled. 1. cavity purge flows and leakage flows were included. Instead using well known thermodynamic properties. (2007) developed a model to study the influence of different air cooling systems. (2008) simulated a four stage gas turbine using a fully three-dim. some pressure drops. Rubechini et al. Typical simplified gas turbine representation. the output temperatures of the turbine are a second degree equation in function of the enthalpy. The fouling of the compressor was widely studied. (2007). Coolant injections. Turbine Ghadimi et al. The combustion was not simulated. Four different gas models were used: three based on gas ideal behaviour (the specific heat Cp evaluation was the difference among them) and one using real gas model with thermodynamic properties (TP) from tables as basis of the modelling. The combustor model considers five components and the combustion reaction stoichiometrics with possibilities of excess of oxygen. A model to diagnose the operation of combined cycle power plants was designed by González-Santaló et al. The inputs are variables like efficiencies. A model for desktop for excel was elaborated by Zhu & Frey (2007) to represent a standard air Brayton cycle.Gas Turbine Power Plant Modelling for Operation Training 171 Combustor Compressor Fig. Navier-Stokes analyses to predict the overall turbine performance. etc. Kaproń & Wydra (2008) designed a model based on gas ideal expansion and compression to optimise the fuel consumption of a combined cycle power plant when the power has to be changed by adjusting the gradient of the generated power change as a function of the weather forecast. In the conclusions the authors point that the results have to be confirmed on the real plant and that main problem is to develop highly accurate plant model. This approach is not useful for a training simulator. (2005) designed a model based on ideal gas to diagnostic software capable of detecting faults like compressor fouling. multistage. the ideal gas assumption was present (Chen et al. For example. component . The governor system model and a simple machine infinite bus were considered (with an automatic voltage regulator model).172 Gas Turbines Even when detailed modelling of the flow through the equipment..combustor –turbine was simulated considering the schematic presented in Figure 2. 1993) there are identified benefits of simulators in four categories: availability savings.5" Bleeding HP 16" VN2 . thermal performance savings. None of the works revised here. Watanabe et al. 2. In this case the gas composition was neglected.. the total plant was simulated. No details of the combustor model are mentioned. including the combustion products and all the auxiliary systems to consider all the variables that the operator may see in his 20 control screens and all the combinations he desires to configure tendency graphs. . 2009). a broader range of personnel can receive effective training. the set compressor. in a classical study made at fossil fuel power plants simulators (Epri. (2010) used Simulink to support a model to analyse the dynamical behaviour of industrial electrical power system. Schematic gas turbine-compressor-combustor diagram. heat transfer phenomena and basing the process on a temperature-entropy diagram. The importance of training based on simulators Some of the significant advantages of using training simulators are: the ability to train on malfunctions. high standard individualised instruction or self-training (with simulation devices designed with these capabilities in mind). In the present work. especially because “what would have happened if…” situations should be addressed. designed for optimisation. and eventually. The model was validated against real data. An ideal gas approach was used. transients and accidents. A cost benefit analysis of simulators is very difficult to be estimated. the reduction of risks of plant equipment and personnel. runs around the full load point. mentioned anything about real time execution. (considering only an increase of the temperature) and the model. The real time execution that is required for a training simulator is accomplished by the IIE simulator. However. 3. Combustor Envelope Combustion gas Air Fuel gas Rotor Air Cooler W10 14" VC1 Atm Pe1 . RC1 P8 NO8 W8 a VN3 3" Temp Cntrl Turb Stage 3 DC3 P7 NO7 W9 b RC3 6" W9 a VN4 4" Temp Cntrl Turb Stage 1 P5 NO5 W11 RC4 Rotor 14" Metals 5 W18 NO9 Metals 4 P9 Metals 3 DC4 GT4 W17 8" Metals 2 W16 Metals 1 W15 DC2 P6 NO6 W14 GT1 VN5 1" Drain Filter W12 Atm Pe1 VC4 GT3 GT2 Discharge Fig. the ability to train personnel on actual plant events. Pa RV1 W1 Pb Filter Bleeding LP VN1 18" P1 CM1 Stages 1 to 6 W5 W6 NO1 W2 P2 CM2 Stages 7 to 10 NO2 W3 P3 CM3 Stages 11 to 16 NO3 W4 VC2 Combustor RV2 Filter Pe2 W9 Fuel W13 VC3 P4 NO4 W8 W7 W8 b RC2 3. operators gain the confidence to bring the plant up and running quicker. (2006) show that in the Geothermal Training Centre. quality and price. Justification also comes from the ability of the simulator to check out the automation system and provide operators with a better understanding of a new process. To provide an excellent service to its clients. Roldán-Villasana et al. This centre attends people that work in fuel fossil generation plants. With greater exposure to the simulator. and simulators for operators’ training. The SD has developed diverse work related with the training. the three of them belong to CFE and have infrastructure developed by the IIE. the justification for acquiring an operator training simulator is based on estimating the reduction in losses (Hosseinpour & Hajihosseini. test equipment simulators. 1998). in a period of 14 years. and the National Centre for Operator’s Training and Qualification (CENAC). To promote the social development. In Mexico exist three training centres based on simulators: the Laguna Verde Nuclear Power Plant Training Centre.Gas Turbine Power Plant Modelling for Operation Training 173 life savings. 2 and 3 summarise the development indicating the year they were delivered to the costumers. commercial. To optimize the utilization of their physical. ensuring to the producers high levels of quality training not only within the technical areas but in all their processes: To guarantee. the number of trips due to human errors and also the percentage of this kind of trips regarding the total numbers of trips have been diminishing through time since 2000 when the Centre began its training program. The CENAC receives in periodical basis information (retrofit) from its users that allows the improvement and development of new training technologies. and human resources infrastructure. The main covered areas by the IIE developments are: computer based training systems. is the main centre in Mexico where the training of the operation personnel based on simulators is achieved. the use of simulators for operators’ training has estimated savings of 750 millions dollars for the power plants (Burgos. considering from adjustments on their training plans to the changes on the scope or development of new simulators to meet the particular needs of the production centres. . in terms of quantity. 2009). Also trains operational workers of the independent producers (that base their production in combined cycle plants). and environmental compliance savings. It is estimated a payback of about three months. the Geothermal Training Centre. according to their statistics for the Cerro Prieto generation plants. the continuous electricity service. The CENAC's commitment is provide excellent services. including combined cycle and gas turbine. thus shortening startups significantly and improving the proficiency of less-experienced operators in existing plants. The operational cost of the training centre is inferior to the cost of the non generated energy because of trips due to human errors (considering only Cerro Prieto power plants). The CENAC. with well-diversified sources of energy. To protect the environment. This is easy to probe for high-capacity plants where savings approach millions of dollars for a few days of lost production. To respect the values of the population who live in the new areas of electrification. a class world company. within a competency framework and updated technology. Most often. Tables 1. Specifically in Mexico. Update of the Simulator System for Tests of Excitation Expanding the Applications of the Simulator System for Tests of Excitation Simulation Module to Test Hydraulic Governors Responses Table 2. the gases are passed through a nozzle. and simulators maintenance and clients support. simulator for training of the operators of a generator experimental rig.174 Computer Based Training Systems Computer-Based Training System Web Version Substation Operator System Training Simulator with a Static Vars Compensator Computer Based Training System by Internet. Testing Equipment Stimulated Simulators Real-time Simulator for Synchronous machines SITIRAMS I. For this particular simulator the unit 5 of the power plant “El Sauz”. module for malfunction analysis of simulated equipments. Virtual Reality System for the Transmission Lines Maintenance Personnel Table 1. Computer based training systems developed by the IIE. SITIRAMS II y III. The choice of this plant was based on the geographical proximity of the plant with the CENAC and IIE installations (to optimise the information compilation) and the availability of the design and operational data. The plant was designed to operate in simple cycle with natural gas only. and mechanically powering the compressor and rotating the generator. It has an upstream air axial flow compressor mechanically coupled to a downstream turbine and a combustion chamber in between. spinning the turbine. duplication of the simulator system for tests for speed control and voltage regulator. In Figure 3 a general view of a gas turbine power plant is presented. and uses a system of low nitrogen oxide emissions DLN2. was selected as the reference plant. The resulting gases are directed over the turbine's blades. Reference plant In order to have a comparison point. located in Querétaro. Energy is released when compressed air is mixed with fuel and it is burned in the combustor. The plant is a pack generation unit Econopac 501F from Westinghouse. The gas compressor-turbine system handles the fuel into a stream of compressed air. in the middle of the Mexican territory. This unit is formed for the gas turbine. In the plant. Finally. . the used fuel is natural gas provides by PEMEX to produce a nominal electric power of 150 MW. The primary equipment consists of a combustion turbine which impulse the hydrogen-cooled generator. all the simulators developed by IIE have a reference plant. national network simulation for the simulator system for tests for speed control and voltage regulator. Gas Turbines Year 2003 2005 2007 2008 Year 1995 1996 2005 2008 2008 Present and near future developments include: a scope extension of the virtual reality system for the transmission lines maintenance personnel. the generator and the auxiliary systems. training centre of hydrocarbon process (with at least eight full scope simulators). generating additional thrust by accelerating the hot exhaust gases by expansion back to atmospheric pressure. Testing Equipment Stimulated Simulators developed by the IIE. 4. 3. . Fig. Simulators for Operators’ Training developed by the IIE.Gas Turbine Power Plant Modelling for Operation Training 175 Year 1984 1991 1991 1993 1994 2003 2006 2006 2006 2006 2006 2007 2009 2009 2009 2009 2009 Simulators for Operators’ Training Simulator I of a 300 MW Thermal-Electric Units Simulator of the Collective Transport System (Metro) of Mexico City Laguna Verde Nuclear Power Plant Simulator Partial Scope Simulator for Turbine Rolling Operations Simulator of a 350 MW Units Simulator of a 110 MW Geo Thermal-Electric Unit Simulator of a 350 MW Dual Unit (Coal and Fuel) Simulator of the Systems of a 300 MW Thermal-Electric Unit Simulator of Thermal-Electric Units Based on Screens Simulator of a 25 MW Geo Thermal-Electric Unit Hydrocarbon Processing Simulator Prototype of a PEP Platform Gas Turbine of a 150 MW Power Plant Simulator Combined Cycle 450 MW Power Plant Simulator Simulator of a Dual Unit with Operation Tracing Simulator of a Combined Cycle Unit with Operation Tracing Simulator for Boilers Analysis Graphic System for the Developments of Simulators Table 3. General view of a gas turbine power plant. fuel gas. It has two 20” flat panel monitors. Also they are the generic models. the simulation sessions are initiated and guided. There exists two Operators’ Stations (OS) that replicate the real control stations from the plant. electric turbine starting. process or control models and where they are tested and validated by an instructor before to install it in the simulator. Control Room Operation Station1 (OS1) Operation Station2 (OS2) Lan switch Maintenance node (MN) Instructor Console (IC) Fig. sealing oil of the generator. The internal reports that sustain these works are not referenced here. The plant is controlled by a Siemens TelepermXP (TXP) Digital Control System. . generator cooling (water/glycol).1 Hardware configuration The gas turbine simulator consist of four PC interconnected through a fast Ethernet local area network. From the Instructor Console (IC). also named simulation node. Configuration of the simulator 5. Figure 4 shows a schematic of this architecture. Also it is used as a backup of the IC.6 GHz. fire system. Each PC has a mini-tower PentiumDTM processor with 3. 5. combustor. ventilation and air conditioning. compressor water wash. Fortran Intel.2 Software configuration The simulator was developed under Windows XP and was programmed in Visual Studio Net. 5. that is used to make modifications to the software. The Simulation Environment (MAS2). equipment for excitation. There is an additional PC. instrument and control air. mechanical package. the maintenance node (MN). Flash and VisSim. compressed air. 40GB HD. 1GB of RAM memory.176 Gas Turbines Other plant systems that support the open cycle are: heating. 4. and Windows XP as operating system. electrical distribution. and generator cooling air. The trainee uses four 20” monitors and two 54” screens to manage and control the simulated power plant. lubrication oil. Figure 5 shows the real simulator architecture (without the MN) during a training session where the IC and the instructor appear in the first plane and the OS and two operators are at the rear. Hardware architecture of the gas turbine simulator. the development 2 The simulation environment is proprietary software of the IIE. and they are communicated through a TCP/IP protocol. with a distributed architecture of PCs or with multi-core equipment. it is constituted for six modules according Figure 6. . Real Time Executive The real time executive coordinates all simulation functions. Training session in the gas turbine simulator. This module executes the IPD. the operator module. The MAS was designed as a general tool for the SD to develop simulators. the operator module. The MAS is a very useful software that acts like a development tool and like the simulator man-machine interface (MMI). and receives/responds from/to the 2. These models may be executed in a parallel scheme. Fig. Each of these modules is hosted in a different PC. with the exception of the Flash applications. 6. DESMM Mathematical model launcher. Diagram of the real time executive application. the models run sequentially. CORDPI Manager module for interactive process diagrams (IPD). and the instructor console module). Its function is to manage the execution sequence of each mathematical model. For the case of the gas turbine simulator. All the modules of the simulation environment are programmed with C# (Visual Studio). 5. provides the values of the variables. and the instructor console.Gas Turbine Power Plant Modelling for Operation Training 177 Fig. The MAS basically consist of three independent but coordinated applications: the real time executive. platform. has three main parts (the real time executive. 1. These values are located in a table loaded in memory for a fast access. to call the methods of each IPD component (valve. 7. This module receives/responds the commands from/to the instructor console (stop. 4. CORCI Manager module for the instructor console. Fig. Other functions of the module are: to control the alarms system. all the required information by the executive system. etc). CORAGD Manager module for the global area of mathematical models. malfunctions.) and executes the tasks in a synchronised way during a simulation cycle. It is composed of a group of methods to initialise the global area of state variables belonging to the mathematical models. This module is also in charge of synchronise the access of the table when parallel process attempt to connect it. to control the historical trends. freeze. 6. control commands messages of the operator console. and to coordinate the sequence of events in the operation consoles. pump. etc. 5. This is the main module of the simulator and coordinates all the functions of the mentioned modules. Main display of the operator console. .178 Gas Turbines 3. CORTR Main module. With the TCP/IP communication. It is devoted to get. from each data base table. this module may be hosted in a different PC of the instructor console. refresh each IPD periodically. MBD Data base driver. The static part is constituted by drawings of particular control screens and the dynamic part is configured with graphic components stored in a library. than may be seen as the MMI are Flash movies inserted in a “Windows way”. 8. The main control screen of the operator (a replica of the Siemens control) is shown in Figure 7. . The IPD. Main display of a tendency graph. These components have their own properties and they are employed during the simulation execution. The main parts of the operator module are: 1. A channel of bidirectional information is established through a TCP/IP socket.Gas Turbine Power Plant Modelling for Operation Training 179 Operator Module The operator module is a replica of the real control screens or IPD and it manages the information flow with the executive system through the CORDPI module. An example of a tendency graph (during a plant trip) is shown in Figure 8. Fig. etc. using the “Fscommand” interface for the communication. The flash movies have both. which are related to each one of the controlled equipments (pumps. valves. static and dynamic parts. including the index. motors. A main module (an “Action-script” code) that loads the interactive process diagrams and gets information about the properties of the movie components. and as many tendencies displays as needed are available for the operator. A total of 20 control screens.). for each MSS the algebraic equations have to be solved simultaneously if necessary but they are mathematically independent of their differential equations. A module to retrieve the static information of the simulation session. for instance. However. 9. thanks that the instructor has a modified copy of the operator control screens where may follow the actions of the students some of them may be accessed from the IPD by special icons. once installed in the simulator. 3. the IIE has adapted different solution methods for both. 5. this was divided into a set of systems (procuring these coincide with the real plant systems). A module to communicate the instructor console with the real-time executive (Console Application).3 Processes and control models To simulate the gas turbine power plant. Instructor Console This module is the MMI of the instructor and has a main menu of functions which is presented in Figure 9. the operator (student) perceives his actions and simulator response in a very close way as it happens in the actual plant. The IC is constituted by five modules: 1. linear and non-linear equations (Newton-Raphson. remote actions. 2. A module for the TCP/IP communications. The differential equations are numerically solved with one of the available methods (Euler. In Section 6. trapezoidal rule with one or two corrections). For the development of simulators. A module to store information in a data base using SQL (DBSM). Fig.180 Gas Turbines 2. A modelled system is a mathematical representation of the behaviour of the variables of the real system of the gas turbine gas power plant. the functions of the IC are fully described. etc. A main module to execute all the tasks related with the graphical interface of the instructor (DPI). The mathematical models. The functions of the IC may be invoked from the list menu of the display with the mouse pointer. malfunctions. respond to the operator’s action in the same way that the real systems do (in tendency and time). The model of a simulated system (MSS). the final equations are stated for each MSS system in such a way the set of equations of one MSS is mathematically independents of the set of equations of any other MSS. 4. (CONINS) 3. Typically. 5. Gaussian elimination and bisection partition search) and are used depending on the structure of each particular model. In the IC the simulation session is controlled. Now. A module to exchange information with the main module and with the executive system. the functions are popped up to be selected. As a result of these functions. The selection of the proper integration method for . Main display of the instructor console. The integration step of the equations depends on the dynamical response of the system. 6.1 “CONTROL” menu (Control) It has the functions that allow the instructor to define the simulator’s status. The sequence matrix was defined using an algorithm to find an appropriated execution order. and the initial period of execution of each model for each cycle. the sequence continues in the same way.2s). step 0. 0. . where the method reports more potential numerical instabilities). from where the simulation sessions are initiated and guided.1 s. For example. the instructor controls and coordinates the scenarios seen by the operator under training. Thus. The sequence matrix (defined by the user) indicates the precedence of execution of the models (scheduler).Gas Turbine Power Plant Modelling for Operation Training 181 a MSS is made running the model under a multistep multirate method to determine its “critical transient” (that.2 s. To perform his tasks. in these control screens some of the IC functions may be accessed from the DPI in special icons. Frames (10 frames is a second or cycle) Model M3 M4 M2 M1 1 3 2 1 1 3 1 2 3 1 2 1 1 3 2 1 1 3 4 5 6 7 8 1 2 1 1 3 2 1 9 10 Table 4. in the second frame model M4 (method 2. if a simulator had four MSS. Each execution second (cycle) of the simulator was divided into ten periods of 0. From there.2s) is executed followed by model M2. An example of the functions displayed by pop-up in presented in Figure 10. the calculation of eigenvectors and eigenvalues and its relation with the state variables). step 0. The algorithm considers the number of inlet and outlet variables between the models and the integration step to minimize the probability of mathematical instabilities.1s). Example of a sequence matrix. The instructor has a modified copy of the operator control screens. Additionally. followed by model M1 (method 3.5 s or 1 s. the functions are popped up to be selected. means that model M2 is the first in being executed in the first frame (it is integrated with the method 1 and has a step of 0. M2.1 s (frames). These scenarios could be presented to the operator as a steady state of the plant operation or under any malfunction of a particular system or equipment. a sequence matrix as defined in Table 4. 0. the IC has a set of functions that may be invoked from the list menu of the display with the mouse pointer. followed by models M2 and M1. in the third frame model M3(method 1. The main functions of the IC are explained in the following sections. step 0. M3 and M4 and three integration methods. the integration method and integration step of each model. A numerical analysis is made on that point to determine the final method and step that the MSS should use (this analysis involves the calculation of Jacobian matrixes. a particular model could be executed with an integration step of 0. 6. Instructor console This is the main MMI for the instructor.5s) is executed. from where can follow the actions of the students. let say M1. to change the description of an ICO.182 Gas Turbines Run/Freeze. slow thermal processes such as the cooling of the plant after a shut down process can be simulated to occur faster. the simulator is executed in real time. or to delete an existing ICO. malfunctions. Fig.2 “CONDICIONES INICIALES” menu (Initial conditions) The initial conditions (ICO) allow: to establish the state of the process at the beginning of the simulation. Simulation of a single step. A simulation session can be repeated automatically including the actions of the operator and the instructor on the simulator. The instructor may start or freeze a dynamic simulation session. to rename an ICO. .1 s). but the instructor may execute the simulator up to ten times faster or ten times slower than real time. and any action are triggered at a specified event or time. 6. Also. For example. Repetition. Normally. 10. this option is useful when the trainee has to analyse a fast transient. to create a new ICO from any simulation instant. therefore the simulator may run in a slow way Automatic Exercises. Example of the functions displayed by pop-up. The instructor may create automatic training exercises where initial conditions. This function activates the simulation for just one simulation step (0. Simulation speed. They may be stored for their subsequent use. etc. Malfunctions. in an automatic way an ICO is registered. They allow the instructor to modify the external conditions: atmospheric pressure and temperature (dry and wet bulb). Examples of them are: pumps trips. When the simulator is running and it is stopped. There are more than 200 of them and they may have time and intensity degree parameters as instructor options. For the binary malfunctions (like trips). besides the mentioned time parameters. As mentioned above. The user may define the total period of time and the frequency of the registration.Gas Turbine Power Plant Modelling for Operation Training 183 Initial Condition. For analogical malfunctions (like percentage of a rupture). voltage and frequency of the external system. External Parameters. Periodicals. These actions are associated with the local actions effected in the plant by an auxiliary worker. Every instructor has associated a directory in which can take or register his own ICO. Such modifications may be effected in an instant or with a delay. according the instructor necessities and preferences. From last stop. . and valves obstructions. and tabulate any list of variables. It is used to introduce/remove a simulated failure of equipments. either from the general pre-selected list or from their own catalogue (each instructor has access up to 100 initial conditions of his own). Remote Actions. The instructor has the option to simulate the operative actions not related with actions on the plant performed from the control screens. This ICO may be established as initial condition. These are the pre-defined ICO. This function creates a file in ASCII format (in a tabular display) of a list of variables defined in other file created by the user (the first column is always the simulation time). monitor and change on line the value of selected global variables. 6. From an instructor. The simulator has an implicit function to register (snapshot) automatically and periodically an ICO. The simulator has a capacity to storage the last twenty snapshots. the instructor has the option of define its time delay and its permanence time. It allows to display and to modify the value of a model on line. The instructor may select an initial condition to begin the simulation session. 6. Examples of them are: to open/close valves and to turn on/off pumps or fans.3 “FUNCIONES DE INSTRUCCIÓN” menu (Instruction functions) The instruction functions allow modify the operation mode of the simulator during a training session. Tabulation. heaters fouling. There are 98 malfunctions available. Values of models variables. fuel composition. This function is currently running during a simulation session and the instructor may define the period of time for each snapshot between 15 seconds and 10 minutes. The client defines how many and which ICO of this kind requires. and any instructor can establish them.4 “SEGUIMIENTO” menu (Tracking) The simulator has a series of very helpful implements especially during the simulation development: simulate just one step (0. heat exchanger tubes breaking. with the main operation states of the simulator. the instructor may define both intensity degree and evolution time.1 s). The ICO may be one of the next: Pre-programmed. by default it is established in two minutes (see Figure 10). It generates a results file in ASCII code for the manipulation of the obtained data. it is also possible to manipulate the ICO or to record a new one. With this function it is possible to create a new account for news instructors. The simulator was developed applying a methodology developed by the IIE. It is possible to modify the variables values. c. The methodology may be summarised as: a. the updating of the simulator may be automatically performed (from excel.5 “MISCELANEOS” menu (Miscellaneous) This menu contains several auxiliary functions that help to the administration of the instruction sessions of every one of the instructors. global variables. some of the modelling tools (concretely some generic models) were developed and/or adapted during the execution of this project. operational plant data. operational curves of the equipment. This button enables and disables the registration of the operators’ actions on the control screens. valves and fittings are automatically obtained in a excel data sheet. . In the diagram the modelled equipment and measurements points are included and it is possible to identify. This function allows changing the instructor account for another without leaving the simulation environment simulation. 7. in order that everybody has their own accounts and the control of his own simulation sessions. Perturbation of a variable. the valves controlled automatically from those operated by the operator or locally. Information of the process is obtained and classified (system description. Simplifications of the system are made obtaining a simplified diagram (showing the simulated equipment with their nomenclature). The information is analyzed and a conceptual model is stated (a functional description of the system). data and code are copied into the programs and data bases of the simulator).). The function also registers the action of the instructor in his MMI. With this function it is possible to have a continuous monitoring window for a group of variables on line. thermal balances. It opens an ASCII window editor to create a file with variables to be tabulated or monitored. system operation guidelines. The configuration of the flow and pressure network is obtained and with the design operational point (normally 100% of load) the parameters of pumps. momentum and mass balances). e. Switch an instructor. This sheet is a part of the final documentation and when it is modified. etc. d. The file can be stored for its future use. This is from 0% to 100% of load including all the possible transients that may be present during an operational session in the real plant. Creation of an instructor account. Main assumptions are stated and justified.184 Gas Turbines Monitoring. The models were designed to work under a full range of performance. In fact. for example. To create a variables group. Modelling methodology The models of the simulated plant were divided in two groups: the control models and the process models. 6. b. Agenda. 7. It allows defining an initial value to a group of variables.1 Processes The models are a set of algebraic and differential equations obtained from the application of basic principles (energy. e. via the digital and analogical exits. Local tests are performed and. parameterisation with excel is performed. The lubrication oil system was next and finally the models of the auxiliary systems (each with its control). Eventually. To prove the successful integration of each model added. An algorithm proposed and used previously in a simulator is to consider an execution sequence trying to minimize the retarded information (variables). All models are integrated into the MAS. The local tests were performed. For example. Global test are made with the needed adjustments. g. these models generate. At this time the MAS included the control screens. an operator achieved some actions on the models. The coupling was done considering the best sequence to avoid as much as possible mathematical problems. i.2 Control The control models acquire and process the actions realized by the operator in the control room by the action on the control screens. As a response. combustor and compressor model with its associated control. Then the generator and electrical grid was added. j.). if necessary. condensers. some adjustments in the models were made. The development of control models was carried out in five stages: . etc. possible changes of the process models. Most of the controls are part of the distributed control system (DCS) by SiemensWestinghouse Power Corporation and some of them are local (out of the distributed control system).) using predefined excel sheets considering the generic models available in the simulator’s libraries or developing the adequate models. The acceptance tests were performed first in the factory and finally in site in both cases with the help of the customer. h. boilers. For the integration. temperatures. Integration between all the different systems and their controls are performed (the coupling order is an important factor). i. For the development of the gas turbine control models the graphics package VisSim was used. The IIE determined the use of this package that had all the necessary modules to develop the modules of the control charts and analog logic simulator. depending of the general condition of the simulated plan. pressures. Final acceptance tests are achieved by the final user according their own procedures. in the MAS the model is run alone and changes in some variables (inputs) are made in order to evaluate the general response of the model. Energy balances are programmed using the required generic models. 7. These diagrams were drawn from the control provider of the real plant that are presented in the format defined by the Scientific Apparatus Makers Association (SAMA). adjustments in the models are made. etc. k. The sources of the information were diagrams provided by the CENAC. Again. the control adjusts the demand of the valves to regulate some variables of the processes around a set point fixed by the operator (levels of tanks. The MAS and its utilities are used for this task. the first model incorporated was the turbine.Gas Turbine Power Plant Modelling for Operation Training 185 f. The calculations of energy balances are programmed following the flow direction and considering possible sets of equations to be solved simultaneously The Equipments out the limits of the hydraulic network are parameterised (tanks. and temperature control. In the plant some equipments are not included in the DCS. which can run in the simulator environment. Gas Turbines Identification of generic control modules. In these cases. load control. Control Modelling. When the information was not available. Control models of the gas turbine simulator. c. The source files of the control models kept in graphic form to facilitate the updates and corrections tests and adjustments. Control Model Prestart and starting logic Combustor Combustor control Lube oil control Auto-unload control Trip logic Generator control Temperature control Pilot & stage control IGV control Flashback temperature monitoring No. temperature monitoring. 1 2 3 4 5 6 7 8 9 10 11 b. The diagrams were transcribed into the VisSim program using the generic modules. malfunctions. Once the diagram was done. the model obtaining procedure was the same that for the SAMA diagrams. the diagram or description of the local controls was sought. Each SAMA control diagram was done into a single VisSim drawing. As a result of this stage 21 control models were detected to be developed which are listed in table 5. a generic graphics library was integrated to create the analog and logic diagrams into the VisSim environment. With generic blocks generated in VisSim. This application generates the variables definitions that are charged into the simulator database (global variables. . Detection of the models not included in the DCS. containing the functions of the SAMA diagrams. Some adjustments to the generated code have to be done with a program developed by the IIE in order to translate the code to C#.). Table 6 presents a part of some C# code obtained from VisSim with the adjustments made by the IIE application. Generic graphical modelling. d. Two hundred SAMA diagrams were reviewed and analyzed to include all the control logic for the pre-start and start permissive. Based on the SAMA diagrams the control models of gas turbine plant simulator were developed. 12 13 14 15 16 17 18 19 20 21 Control Model System DLN control Rotor cooling control Simulation/Test VARS/PF control System alarms Supervisory turbine Counter and timer logic Air instrument control Electrical system Graphic trends No.186 a. As an example. Table 5. remote functions. Translation from VisSim into C # language. Figure 11 shows the generic modules that were developed in VisSim. e. speed control. From control system diagram in VisSim an ANSI C code is automatically generated. Figures 12 and 13 show the diagram of speed control loop in the original SAMA version and in the VisSim drawing. the control diagrams were developed and accorded with the client. etc. Compressed Air. Air for Instruments. Modelling development 8. The systems included in the simulator are (each with its associated control systems): Fuel Gas. The main important characteristic of each simulated system is that it is controlled from the main control screens. 8. Water- . Control Oil. Generic graphics library for the SAMA diagrams modelling in the VisSim environment. Lubrication Oil. from the process itself (trough remote functions in the simulator) or from the DCS. and that has an impact on the global plant status. Gas Turbine.1 Simulated systems The systems that finally are simulated were selected in order to have all the information the instructor needs to train an operator. 11.Gas Turbine Power Plant Modelling for Operation Training 187 Fig. 188 Gas Turbines Fig. 13. VisSim diagram for the turbine speed control loop. 12. Original SAMA diagram for the turbine speed control loop. . Fig. Gas Turbine Power Plant Modelling for Operation Training 189 Ethylene Glycol. Example of C# code generated automatically from the design diagrams.2 Generic models The design of generic models (GM) allows reducing the time used to develop a simulator. For the case of a training simulation. the disc cavity temperatures (with 8 displays) and emissions. Table 6. Performance Calculations (Heat Rate and Efficiencies). Cooling. which represent a “global” equipment or system and can facilitate its adaptation to a particular case. the exhaust temperatures (with 16 displays). . A GM may be re-used for several applications (either in the same simulator or in different simulators). 8. Electrical Network. Generator Cooling with Hydrogen. including the combustor blade path temperatures (with 32 display values). Turbine (Metals Temperatures and Vibrations). a GM constitutes a standard tool with some built-in elements (in this case. and Combustor. routines). Generator. air and combustion products. The independent variables are associated with the operator’s actions (open or close a valve.2 P (1) where T is temperature. The functions are applied to three different cases: subcooled liquid saturated and superheated steam. the equations (3) and (4) were slightly modified in some regions of P. The application range of the functions is between 0.3 + kt . i = ks . and the specific point (liquid or steam) where the calculation is made. i P (4) To ensure an relative error less than 1%. The same functions may be used if the independent variables are P and T. h . h . trip a pump manually.5 P 2 For subcooled liquid and superheated steam. The densities ρ of saturated liquid and steam are calculated as: ρ = kt .) and with the control signal from the DCS. to achieve this it was necessary to divide the region into 14 pressure zones.3 h 2 (2) (3) where: ´ ´´ k s .190 Gas Turbines Fundamental conservation principles were used considering a lumped parameters approach and widely available and accepted empirical relations. The transport properties (viscosity. heat capacity. and thermal conductivity) are calculated for liquid. both the liquid and steam properties are only a function of pressure and they are calculated as follow: (T .i has different values according to the calculated TP. s is entropy. the pressure region.1 + ks . In this case. i + ks . the functions are: (T .1 + kt . thermal expansion.1 and kt. the calculation is based in seven cubic state and corresponding states equations to predict the equilibrium liquid-steam and properties for pure fluids and .i and ks. For this simulator the hydrocarbon TP were applied for the gas fuel. steam and air with polynomial functions up to fourth degree (for different P and T regions). The adjustment was performed to assure a maximum error of 1% respecting the reference data. ρ ) = ks .4 P + kt . kt. The functions were adjusted by least square method.1 psia and 4520 psia for pressure. Physical Properties The physical properties are calculated as thermodynamic properties for water (liquid and steam) and hydrocarbon mixtures and transport properties for water. For the saturation region. and -10 0C and 720 0C (equivalent to 0.2 h + ks . steam and air. s .18 BTU/lb and 1635 BTU/lb of enthalpy). For the water the TP were adjusted as a function of pressure (P) and enthalpy (h). etc. The data source was the steam tables by Arnold (1967). The functions also calculate dTP/dP for the saturation region and ∂TP/∂P and ∂TP/∂h for the subcooled liquid and superheated steam. The calculation is done for finding the unknown variable (or value) from equations (1) to (4). s ) = kt .2 are constants to determinate the particular TP and depends of the phase (liquid or vapour). Note: In all cases kt. w. pumps. n-heptane. considering all the inlet (i) and output (o) flowrates (w): Σwi − Σwo = 0 (8) Also. Tr Z( R ) = Pr Vr ( R ) . the Newton-Raphson method is used. the momentum equation may be applied on each accessory on the flow direction x: ρ ∂v ∂P ∂τ x x ∂v =. The accessories are those devices in lines that drop or arise the pressure and/or enthalpy of the fluid (valves. nitrogen dioxide. Peng-Robinson. and a. An external node is a point in the network where the pressure is known at any time. nodes (junctions and splitters) and lines (or pipes). Racket (for saturated liquid only). Soave. C. and Ideal Gas. Lee-Kesler. A line links two nodes. u. Redlich-Kwong. heat exchangers and other fittings). 1987): P= RT a − ˆ − b v2 + u v b + w b2 ˆ ˆ v (5) ˆ where R is the ideal gas constant. nitrogen monoxide. β. A convenient approach to represent the network (easy to solve and sufficiently exact for training purposes) is considering that a hydraulic network is formed by accessories (fittings).ρ vx x + ρ gx ∂t ∂x ∂x ∂x (9) . n-pentane.. methane. n-octane. and water. and γ are characteristics (constants). carbon monoxide. The model is derived from the continuity equation on each of the nodes. oxygen. Tr Z = Z(0) + (7) where B. An internal node is a junction or split of two or more lines. There are 20 components considered that possibly may be form a mixture: nitrogen. v is molar volume. C4. Hankinson-BrobstThompson (for liquid only). Flows and Pressures Networks This model simulates any hydraulic network in order to know the values of the flows and the pressures along the system. n-hexane. The validity range is for low pressure to 80 bars. and Ω is Pitzer's acentric factor. sulphur dioxide. The cubical equations have the following general form (Reid et al. b. ethane. A node may be internal or external. carbon dioxide.Gas Turbine Power Plant Modelling for Operation Training 191 mixtures containing non polar substances. turbines. Also may be used the corresponding states equation Lee Kesler: Z( o ) = 1 + B Vr (0) + C (Vr (0) 2 ) + D (Vr (0) 5 ) + C4 Tr (Vr 3 (0) 2 ⎡ ⎡ −γ ⎤ γ ⎤ exp ⎢ (0) 2 ⎥ ⎢β + (0) 2 ⎥ ) ⎢ (Vr ) ⎥ ⎢ (Vr ) ⎥ ⎣ ⎦ ⎣ ⎦ Ω (Z( R ) − Z(0) ) ΩR (6) Z(0) = Pr Vr (0) . are constants that in fact determine the precise cubic equation that may be used: Van der Waals. nnonane. these nodes are sources or sinks of flow (inertial nodes). D. i-butane. piping. hydrogen sulphide. n-butane. filters. For the solution of any of the equations for a gas mixture. ndecane. propane. ). The error dismisses if more straight lines were “fitted” to the curve. The exponent ζ represents the characteristic behaviour of a valve in order to simulate the effect of the relation between the aperture and the flow area. This line is represented as: ΔP = m' w + b' (14) If there are two or more accessories connected in series and/or two or more lines in parallel are present. but the model allows for any number of them. To exemplify the linearization approach. an equivalent equation may be stated: ΔP = m w + b (15) . Similar equations may be obtained for any other fitting (turbines. equation (13) is selected for the case of a pump with arbitrary numerical values (but the same result may be obtained for any other accessory and any numerical scale). In this case two straight lines are used to simplify the explanation. etc. The aperture applies only for valves or may represent a variable resistance factor to the flow (for example when a filter is getting dirty). that the forces acting on the fluid are instantly balanced. For example. Note that the density ρ has a much more influence on a compressor than a pump. the pressure drop may be approximated by the correspondent straight line (between two limit flows of this line). the flowrate pressure drop (ΔP) relationship is: w 2 = k ' ρ Apζ ( ΔP + ρ g Δz ) (11) where the flow resistance is a function of the valve aperture Ap and a constant k´ that depends on the valve itself (size. filters.2. and speed are constant. a model may be stated integrating the equation along a stream: ΔP = − L Δτ + ρ g h (10) where the viscous stress tensor term may be evaluated using empirical expressions for any kind of accessories. If it is considered that in a given moment the aperture. density. Figure 14 presents the quadratic curve of flowrate w on the x axis and ΔP on the y axis (dotted line).192 Gas Turbines Considering that the temporal and space acceleration terms are not significant. a more efficient way to get a solution is achieved if equation (13) is linearised. for a valve. For a fitting with constant resistance the term Apζ does not exist. In the curve two straight lines may be defined as AB and BC and represent an approximation of the curve. However.3) are constants that fit the pump behaviour. For a given flow w. etc. For a pump (or a compressor).). type. piping. this relationship may be expressed as: ' ' ' ΔP = k1 w2 + k2 w ω + k3 ω 2 − ρ g h (12) where ω is the pump speed and where k´i (for i=1. both equations (4) and (5) may be written as: w 2 = ka ΔP + kb (13) Applying equation (8) on each node and equation (13) on each accessory a set of equations is obtained to be solved simultaneously. a linear equations system is obtained where pressures are the unknowns. In the flows and pressures GM an algorithm to detect the active topology is detected in order to construct and solve only the equations related to the particular topology each integration time. i.e. 14. The order of the matrix that represents the equations system is equal to the number of internal nodes of the network. Linearization of the curve that represent a fitting. The procedure seeks the system of equations to identify the sub-systems that can be solved independently. The active topology may change. The valves are considered with an isoenthalpic behaviour and the compressor and turbine are calculated as an isoentropic expansion and corrected with an efficiency. For example. This equation may be arranged as: w = C ΔP + Z (16) Substituting equation (16) on (8). To obtain a numerical solution of the model is convenient to count with a procedure that guarantees a solution in any case. (2004) in detail. for each flow stream. Flows are calculated by equation (16) once the pressures were solved. The solution method is reported by Mendoza-Alegría et al. During a session of dynamic simulation a system may change its active topology depending on the operator’s actions. This means that the order of matrix associated to the equations that represent the system changes. the . avoiding the singularity problem and that helps the understanding and development of models of simulators for training purposes. for instance.Gas Turbine Power Plant Modelling for Operation Training 193 250 200 A B Pressure Drop ΔP 150 100 50 0 0 5 10 C 15 20 25 30 35 Flowrate w Fig. The full topology is that theoretical presented if all streams allow flow through them. if a stream is “created” or “eliminated” of the network because a valve is opened and/or closed or pumps are turned on or off. An active topology of a network is a particular arrangement of the grid that allows flow through their elements. To exemplify a flows and pressures network. Figures 16 and 17 present the simplified diagrams of the flows and pressures networks of the generator’s cooling water and hydrogen supply. Then. respectively.194 Gas Turbines properties at the compressor’s exhaust are calculated as an isentropic stage by a numerical Newton-Raphson method (i. Pe . c ) = 0 (17) where c is the gas composition. These simplified diagrams are the basis to parameterise the flows and pressures GM according the methodology developed by the IIE. Control and display screen of the generator cooling water and hydrogen supply. the leaving enthalpy is corrected with the efficiency of the compressor: he = * ( he − hi ) η + hi (18) All other exhaust properties are computed with the real enthalpy and pressure. The efficiency η is a function of the flow through the turbine. . c ) − se (Te* . 15. The properties at the turbine exit were formulated like the compressor but considering that the work is produced instead of consumed. Fig. in Figure 15 the control screen from the OS for the water cooling system of the generator and the hydrogen supply is reproduced. the isoenthalpic exhaust temperature Te* is calculated at the exhaust pressure Pe with the entropy inlet si): * f (Te* ) = si (Ti . Pi .e. . . The model to simulate electrical grids was adapted from the generic model for hydraulic networks (Roldán-Villasana & Mendoza-Alegría. The control screen of the electric network is presented in Figure 18. . conductances (C) by admittances (Y). VN3 W3 P2 W3a VN6 W3b VN8 VN10 W3d NO2 W3c Pk VN4 Pump 2 VN5 VN12 Pm .2 RC2 Cooler 2 dray. P60 Pe1 VN1 RC1 P2 P61 Pe2 Fig. The . . Pg Pi Cooler. Simplified diagram of the generator hydrogen supply.Gas Turbine Power Plant Modelling for Operation Training W5b C O O LER 195 VN14 .1 RC1 Cooler 1 dray . . . 16. equations (8) and (16) may represent an electrical network in a permanent sinusoidal state by substituting flows (w) by currents (I). and valve apertures (Ap) by a parameter to represent the variation of a resistance or impedance (Ps). Simplified diagram of the generator cooling water system. Although the model was designed to represent alternate current grids.2 RC4 .1 RC3 Cooler. Pd P5 NO5 Pump 1 Pa BO 1 BO2 NO6 P6 . No linearization was necessary because the electric equations are linear. . Electric Phenomena Model The generator model is not discussed here but it was simulated considering a sixth order model and equations related to the magnetic saturation of the air gap. 1 dray . Po W6 VC1 Pc VC2 Pf W8 RC5 VN16 W5a P4 NO4 VN15 VN18 W2 W1 TANK VN2 NO1 P60 Pe1 VN19 VN1 P1 W7 . pressures (P) by voltages (V). . the residual magnetism and the effect of the speed variations on the voltage. it is able to represent direct current circuits. 2004). pumping terms (Z) by voltage source increase (VT) when they exist and considering that the gravitational term does not exist in electrical phenomena. Ph Pj Pl Pn W4b VN7 VN9 VN11 VN13 NO3 W4a W4 P3 Fig. P62 Pe3 w3 P VC2 VN5 w1 TANK w2A VC1 NO1 VN4 VN2 P1 w2B VN3 NO2 H2 supply w4 GEN. The first adaptation was made considering that it was necessary to handle complex numbers. 2 dray. 17. Basically. Control screen of the electrical network. . 18. the dynamics of speed and electrical current of the electrical motors are calculated. The current I is simulated by the adjustment of typical curves of the motor (speed ω. (1997) were adopted (an variation of the routines was effected to perform the inversion of the matrix in order to report the Thevenin equivalent impedances). including the surge overcurrent at the startup of the motors. In Figure 19. algorithms proposed by Press et al. Motors From design data. electrical current. One enhancement to satisfy a special requirement of electrical networks was accomplished: to not consider the branches as having closed switches (branches with practically no resistance). the schematics diagram (for parameterisation) of the electric network is shown.196 Gas Turbines Fig. slip and torques) in a simplified form to show the current’s peak during the motor start up: I= ki + kii ω (19) The speed is calculated by the integration of its derivative which is an equation that fits the real behaviour of the motor. dω = (ωnom − ω ) kiii dt (20) The variable ωnom is nominal speed if the motor is on and is zero if the motor is off. The constant kiii has two values one for the motor starting up and other value for the coast down.Gas Turbine Power Plant Modelling for Operation Training S12 NO5 197 S14 I 10 S11 S10 I8 NO3 NO6 I 11 R6 Ve3 Regulation Module S7 Ve10 Ve11 Other units I7 S8 S9 NO4 I 23 S31 R16 S30 NO10 R17 I 24 S32 S4 R3 I3 I9 S13 R5 S6 Ve4 5 MW I4 NO2 I6 I5 I 14 NO11 NO1 S2 S3 S5 S18 R4 NO7 I 12 S15 NO8 R8 S16 I 13 I 22 I 16 S20 Ve8 I2 S1 R2 R1 I1 Ve5 Start motor S17 R7 I 15 S19 R9 S21 Ve2 Ve1 D1 NO9 I 18B I 18A D3 S23 S25 R12 R14 I 20 NO14 Other units I 21 S27 S28 S26 S29 Ve6 I 17 S22 R10 I 27 NO12 I 19 R13 D2 R11 S24 Aux. NO13 Ve12 R20 Ve14 Batteries Ve13 Fig. 19. Simplified diagram of the electric network as used for parameterisation. The heat gained by the fluid due the pumping Δhpump when goes trough a pump (turned on) is: . Ve7 S34 R18 I 26 R21 I 28 I 29 1 27 V To BOP I 25 R19 S33 Ve8 Ve9 R15 1 4 2 5 8 0 3 6 9 7 Start plugs Aux. however. The concentration of each species j is calculated as the fraction of the mass mj divided by the total mass m in a node.198 ⎛ η ΔP ⎞ Δhpump = ⎜ ⎟ ⎝ ρ ⎠ Gas Turbines (21) where η is the efficiency. m is the mass of the node. the inertial variables are the enthalpy h. The subindex i represent the inlet conditions of the different flowstreams converging to the node. However. the pressure is calculated using next equation obtained with basis in an ideal gas behaviour (only the pressure change is calculated as an ideal gas. These equipments were not used in this simulator and their formulations are not explained here. The state variable could be the temperature if no phase change is expected and if the specific heat Cp divides the qatm term. and qatm the heat lost to the atmosphere. j − ∑ wo c j (24) The second kind of node is those that is a frontier of the flows and pressures network. two approaches are used: the simplified model used for capacitive junction nodes or gas contained in close recipients (no phase change is considered in this discussion but indeed a generic model is available). In this case. With the enthalpy and pressure it is possible to verify if the node is a single or a two phase one (for the case of water/steam). The first one is a node that is part of the flows and pressures network whose pressure is calculated as explained before. The mass of each component is calculated by integrating next equation: dm j dt = ∑ wi ci . and complex gas processes like a combustion chamber. condenser. Here. All the steam mass balances are automatically accomplished by the flows and pressures network solution. In this category are the boilers. and other equipments related with different phenomena involving water/steam operations. For the simplified model. not the other properties): . regarding gas processes. An energy balance on the flows and pressures network is made where heat exchangers exist and in the nodes where a temperature or enthalpy is required to be displayed or to be used in further calculations. The temperature at the exit of the pump To is (being Ti the inlet temperature): To = Ti + Δhpump Cp (22) Capacitive Nodes There are two kinds of capacitive nodes. and the composition of all the components cj is necessary in order to determinate all the variables of the node: dh = dt ∑ wi ( hi − h ) m − q atm (23) In this equation. the concentration of the gas components must be considered through the network. the state variables depend on each particular case. deaerators. The representative temperature difference between hot (h) and cold (c) streams is.i ) ⎛ T − Tc . metals cooled with hydrogen. Equation (23) for the enthalpy is used too. Equation (23) applies for temperature (or enthalpy) variations and a mass balance is used to calculate the derivative of the liquid mass: dm = ∑ wi − ∑ wo dt Where the liquid volume is: Vl = m (27) ρ (28) The liquid level is calculated with an adequate correlation depending on the tank’s geometry. The fluid-air exchangers were modelled considering a heat flow q between the fluid and air: q = U A ΔT (29) The heat transfer coefficient U depends on the fluids properties. some extra calculations are made to known the liquid and vapour volumes. the internal energy and density are known (this later by dividing the total mass and the volume of the node). A last category of capacity nodes are tanks that are open to the atmosphere and filled with liquid. being this a state variable too as indicated in equation (24) with the molecular weight. the logarithmic mean temperature difference calculated as (for countercurrent arrangements): ΔT = (Th . so all the properties are calculated with a double Newton-Raphson iterative method. three varieties of heat exchangers were included: fluid (gas or water) cooled by air. flowrates. The thermodynamic properties are a function of pressure and temperature. but this is not treated here.Gas Turbine Power Plant Modelling for Operation Training 199 P= n RT V (25) The change in the moles n of the nodes is obtained correcting the change of the mass.i ⎝ ⎞ ⎟ ⎟ ⎠ (30) . air or oil. o Log ⎜ h . For complex processes where a possible change of phase occurs. and the construction parameters of the equipment. When two phases are present. Heat Exchangers In the simulated plant. generally. A is the heat transfer area. o ) − (Th .i ⎜ Th .i − Tc . Here. o − Tc . the model considers to calculate the internal energy u in the node and its pressure. and water-water exchangers. o − Tc . The derivative of the internal energy is evaluated as: du = dt ∑ wi hi − ∑ wo h − u m dm − q atm dt (26) The derivative of the total mass is the sum of the derivatives of each species as equation (24). With the new heat. air or oil. etc. is equivalent to the cooler temperature Tf. So. 20. it is necessary to accomplish the thermodynamics’ second law by avoiding the crossing of the temperatures in the exchanger. If a crossing of temperatures is detected. depending of which is the cold and the hot streams and the maximum heat allowed by each stream to no violate the second law. and the exchanger is a fluid-fluid one.200 Gas Turbines and for each fluid. a energy balance may be stated (with a constant Cp) to calculate the exit temperature (exit enthalpy also may be used if a constant Cp is not considered ⎛ q ⎞ To = Ti − ⎜ ⎜ wCp ⎟ ⎟ ⎝ ⎠ (31) Besides. Tg is represented by virtual temperatures (TI for the current and Tω for the speed) that are calculated in order to simulate theses heating effects (a scheme of the heat transfer process is shown in Figure 20): Tg qg qatm Tm qf Tf Fig. Schematic representation of a generic metal-fluid heat exchange. considering a minimal temperature differences (defined by the user) between the hot and cold streams: the outlet temperature of the cold stream does not be warmer than the inlet temperature of the hot stream and the outlet temperature of the hot stream does not be colder than the inlet temperature of the cold stream. or another fluid (radiators). electric current (generators and motors). when the metal is heated by a fluid. when the dynamics is relatively slow. the heat is calculated arranging the equation (31). Clearly. clearly the heat calculated by equation (29) is too high and the limiting stream is identified. The model for the metals cooled with hydrogen. the outlet temperatures are calculated again. When the metal is heated by friction or electrical current.). motors. compressors. The generated temperature Tg. was based on the fact that the metal is heated by friction (turbines. an iterative procedure may be established in order to converge the last three equations with this procedure. ' TI = Tamb + kI I (32) (33) ' Tω = Tamb + kωω . This approach is used instead equations (29) to (31). 19 NO2 + 0m18.4 CO2 + 2m5.2 O2 1m19.20 SO2 1m4.16 H2O + 0m5. Combustor A GM for the combustor was developed by the IIE.2 O2 1n19.1 CO + 0.3 H2S + 1m3. some of the reactions for the combustion process are: 2n1.17 CO (37) m15. for example production of .1 is defined as the fraction of the theoretically amount of oxygen that is consumed for a total combustion (is 1 if a complete combustion reaction is hold. The objective is to calculate flame temperature and the composition of the burned gases.1 H2S + 1. thus.19 NO2 1m20.1 SO2 Water should be considered joining external flow to control the chamber temperature (to prevent emissions) and the humidity contained in the fuel.2 O2 1n4.2 O2 + 0m1.2 O2 + 0m5. To calculate the flame temperature the stoichiometric coefficients are needed.16 H2O 1m17.1 NO + 0.20SO2 10n15.1 H2O 1n17.2 O2 n2.4 CO2 + m15.2 O2 0m3.15 C10H22 + 0m15. including the generator cooling with hydrogen that contains several heat exchanging stages. gas fuel and combustion products.16 H2O + 0m15.17 CO 2m16. the temperature of the metal may be calculated by integration of next equation: dTm q g − q f − q atm = dt Cpm mm (35) qf is calculated using equation (29) but the temperature difference ΔT is: ΔT = Tm − T f (36) With this approaches any heat exchanger may be simulated.1 CH4 + 2n5.19 NO2 m2.Gas Turbine Power Plant Modelling for Operation Training 201 Thus.2 O2 n18.1 O2 1n3. The excess of oxygen may be calculated from the flowrates of the reactive components. It is possible simulate a mixture up to the same 20 components of the thermodynamic properties for the air.2 O2 + 0m15.1 N2 + 4n1.17 CO + 0m17.4 CO2 1m5.4 CO2 + 0m17.16 H2O + 1m3. it is possible to calculate the total generated heat qg by speed qω and current qI to the metal using a proper correlation for the heat transfer coefficients (Pasquantonio & Macchi.5 CH4 + 0m5.1 N2 + 0m1.2 O2 + 0m3.18 NO + 4m1. 1976): q g = qω + q I = kω (Tω − Tm )ω 0.1 CO2 1n5.2 O2 2n16.2 O2 1m18.18 NO + 0m18.1 C10H22 + 155 n15. The total combustion efficiency αi.5n17.4 + kI (TI − Tm )I 2 (34) So.2 O2 • • • 0m1.5n3.5n18.1 NO2 1n20. 1 = 0.202 Gas Turbines CO2 and 0 if none of the products of a reaction is completely oxidized).19 (40) Similar equations may be stated for the oxidation reaction of each component and all the coefficients may be calculated.2 = 0. Thus. and heat losses by radiation and convection.18 + 1 m1. Although no kinetics is taken into account. but any equation could be defined). m1.1 = 0. This formulation may be applied in a generic way for any quantity and any number of reactants. based on the excess of oxygen (a thumb rule.19 = 2 α1.2 ≤ 1 (38) must be satisfied at any moment. As an example the equations to obtain the stoichiometric coefficients related with the nitrogen (and the oxygen in the nitrogen reaction) are: N : 2 n1. to avoid imbalance problems.2 = 0.1 n1.1 α1. The reactive stoichiometric coefficients n are known variables except for the oxygen. as presented in Figure 21.5 m1.2 = 0.0 . α1.0 . a linear interpolation is used between the boundaries.2 = 0.1 .1 = 2 m1.0 If excess of oxygen = 100% α1. An iterative process may be followed to find the flame temperature as a function of the amount of all the present species considering: the heat of combustion (automatically calculated from the component’s formation heats). The partial combustion efficiency αi.19 . Local Controls During the off line tests. a linear function was defined for each efficiency (and for each reaction).1 – m1. α1.2 = 0. The efficiencies are normally not constant and any function could be adjusted but considering that. With the coefficient m. α1.2 n1.1 + m1. the restriction αi. this approach considering these original two efficiencies. the models run without the DCS (see Section 9).0 If excess of oxygen <= 50% (39) Here. allows simulate the behaviour of the combustor.5 m1.2 = 0.1 m1.19 ) n1. for example production of CO and 0 if none of the products of a reaction is partially oxidised).19 O2 : n1.18 + m1.18 = 2 α1.1 = 0.1 + αi. The combustor is considered to be a capacitive node and equations (24) and (26) applies for the calculation of the combustor variables considering that the product of the combustion is the inlet to the capacitive node equations and the concentration in the combustor are associated to the exit flowrate. thus. independent local controls applied on valves were simulated in a simplified way to avoid the problem of . for the nitrogen oxidation: m1.1 m1.18 – m1.0 If excess of oxygen >= 200% α1. the concentration of the product is obtained. For this particular application of the combustor model. reactive and product sensitive heat.5 ( 2 n1.18 + m1.2 is defined as the fraction of the theoretically amount of oxygen that is consumed for a partial total combustion (is 1 if partial oxidised products are generated.1 = 0. some assumptions and simplifications are involved in the final models. Va the value of the variable to be controlled. Inevitably. Although first principle and well known tested and approved correlations are used as the modelling basis. and.3 Malfunctions. air cooled condensers. remote functions and external parameters Malfunctions. differences between the model results and the plant behaviour are presented. the parameters have to be adjusted. valves failure (open. . separators of hydrocarbon mixtures. etc. The simulator resulted with 1500 parameters. close or stuck). 8800 global variables including 33 analogical malfunctions. Conceptual model of the combustor. They may be classified in the types generic and specials. in all cases worked with enough precision for the tests purposes (in fact. 55 analogical remote functions and 151 binary remote functions 8. temperature and flow transmitters. Final Remarks There were not included in this revision the generic models developed by the IIE that were not utilised in this simulator as ejectors. the model has been applied on the final version of other full scope training simulators). filters and flow resistances fouling. deaerators. heat exchanger fouling (to decrease the heat transfer coefficient). Generic malfunctions: problems in the pressure. The model for the aperture demand dm is: dm = Ap ± k p Sp − Va Sp (41) Where Sp is the desired set point. 65 logical malfunctions. 21.Gas Turbine Power Plant Modelling for Operation Training 203 Combustor Fuel gas Gas and air Compressor Reaction Reaction products Flame Temperature Combustor exit components Combustor pressure and temperature Turbine Capacitive node Fig. boilers. Kp is a proportional constant whose value depends on the dynamics of the controlled variable. To fit the model in order to minimize the difference to accomplish with the ANSI/ISA norm. a variable increased or diminished because it is not being controlled. The aperture of the valve tends to the value of the demand with a lag (kt) as: Ap = Ap + ( dm − Ap ) kt (42) Although the control model is not a conventional one and there does not exit an integral value. alteration of the turbine and generator vibrations. cooling tower. The malfunctions included in the simulator were defined according the ANSI/ISA norm and the particular interest of the CENAC. ). External parameters. i. exhaust thermocouples). Remote functions The remote functions included in the simulator were defined according the ANSI/ISA norm and the particular interest of the CENAC. and assure that all the models . motors trips (for pumps. operator console. fault of the control components (turbine overspeed. combustion factor and variation in the voltage and frequency of the external system. and instructor console. The external parameters allow modifying the environment conditions that do not depend on the operators control as: temperature (dry and wet bulbs).204 System Subsystem Number of malfunctions Gas Turbines Number of remote functions C1 Control System Supervisory System Generator and Electric System Gas Turbine Ready to Start/Trips C1 Gen Vibrat Analysis C1 Combustion Flash back C1 Blade Path Exhaust Fuel Gas System C1 Lube Oil System 13 7 1 4 3 36 7 5 2 2 2 16 64 7 5 0 0 0 4 35 18 32 15 26 Auxiliary Systems C1 Hydr Ctl Oil System C1 Generator Longitudinal C1 Gen Seal Oil System C1 Turbine Cooling System Table 7. In Table 7 the number of malfunctions and remote functions are listed according the systemsubsystem classification defined by the customer to be presented in the respective simulator pop-up menu.). a very important task is to define the causal relation of the models. etc. and set point modification. to specify for each model all the variables (inputs and outputs) between the models. problems in the combustor (low combustion efficiency. gas supply pressure. heat exchanger tubes breaking. 9. etc. They are the malfunctions specifically designed to cover the CENAC’s necessities: malfunctions of electric components (black out. charge of generation rejection. atmospheric pressure. and start up and trip of equipments. low pressure of fuel gas supply. fans. The main remote functions are: opening and closing of manual valves.). and closed tanks gas leaking. opening and closing of switches and relays. variation of the metal temperatures in the turbine-generator metals. Off line testing and coupling of the systems models During the models development. compressors etc. controls. and turbine low efficiency. and both methane and nitrogen molar fraction in the gas. selection of the equipment. no detection of the combustor flame. Number of malfunctions and remote functions for each system in the simulator.e. automatic and manual position switching. Special Malfunctions. Gas Turbine Power Plant Modelling for Operation Training 205 have congruency. In Table 8 a list of the events and the time they happen is presented. The customer provided the plant data for an automatic start up procedure (with a total of 302 variables). the DCS models are integrated into the MAS without the process models and tested to verify its dynamics. The tests included all the normal operation range. For the coupling process. The idea of the tests is to reproduce the design data. The gas delivery pressure is measured in a pressure controlled header where the gas is stored from a duct that delivers the gas continuously. Fabric tests are applied (the same mentioned in the following section) to the integrated simulator before it is translated to its final site in the customer’s facilities. the combustor pressure is presented on the left y axis and the gas delivery pressure (an external parameter where the operator has no control) is presented on the right y axis. In all the tests may be appreciated the good agreement between the real plant data and the simulation results. is tested off line without controls (open loop). In all cases the response satisfied the ANSI/ISA norm. This data base contains the variables declaration for the C and FORTRAN programs. a comparison between the real plant values and the simulator results during the first 2780 s are presented. including the control screens. In this stage adjustments are done. then no plant data are available and only the simulator results are displayed up to the end of the simulation. The simulator results were compared with these data. instruments ranges. The variables (global variables) are classified and added into a data base. 10. When the last model has been added and the 100% initial condition is ready. No further commentaries are necessary at this respect. from cold start conditions to full charge. In this stage it is convenient to have some simplified controls to avoid problems of process instabilities. . for example in a tank model it is necessary to control the level to avoid it becomes empty or shedding. For all the graphs. etc. including the response under malfunctions and abnormal operation procedures. developed independently. by operating the plant there are obtained all the other initial conditions up to get the cold start initial condition. normally data plant working at 100% of capacity. excepting Figure 22. The plotted variables were chosen to verify the effect of the malfunctions. The global input variables must have an initial values registered in an ASCII format file (initial condition). remote functions. During these transients no actions of the operator were allowed. to avoid mathematical instabilities. (“Acceptance Simulator Test Procedures”). To selected results presented here are an automatic start-up followed by a coupling of malfunctions. Each MSS. No data for other transients were considered as design data. In Figure 22 a comparison between the expected and simulator turbine speed is presented during the turbine speed up during 830 s when the speed reaches its nominal value of 3600 rpm. In Figure 23. parameters values. malfunctions. The models are added one by one according the defined sequence matrix. unit conversions. Validation and results The simulator validation was carried out proving its response against the 16 very detailed operation procedures elaborated by CFE specialised personnel. With each model the initial condition file is actualised and some tests are performed to assure the coupling is successful. The behaviour of the combustor pressure is explained in Table 9. one for the pilots and three more that distribute the flow around the combustor inlet nozzles. Malfunction of low efficiency in the combustor takes its final value (50% of severity). The plant produces its nominal charge (150 MW). Turbine reaches its nominal speed (3600 rpm). 22. End of the simulation. Table 8.206 Time (s) Time (hh:mm:ss) Event Gas Turbines 0 5 120 830 2790 2970 3000 3500 3680 4200 00:00:00 00:00:05 00:02:00 00:13:50 00:46:30 00:49:30 00:50:00 00:58:20 01:01:20 01:10:00 Simulation is initiated. Initiates malfunction of pressure loss in the delivery line of gas fuel. There exist four gas control valves. In Figure 24. Turbine speed comparison for the real plant and the simulation. Malfunction of pressure loss in the delivery line of gas fuel takes its final value (4082 kPa). Times of the transients’ events The graph of the gas delivery pressure (Figure 23) shows how the pressure changed with a ramp between the 3500 s and 3680 s. Turbine is turned on in automatic mode. 3600 3000 Real Plant Simulator Speed (rpm) 2400 1800 1200 600 0 0 150 300 450 600 750 900 Time (s) Fig. the fuel gas flowrate is plotted on the left y axis and the apertures of two (A and C) of the gas control valve apertures are presented on the right y axis. . All they open in a prefixed sequence and their function is to control the turbine speed and the produced electrical power. Ignition in the combustor is triggered. Initiates malfunction of low efficiency in the combustor. 4200 Table 9.3680 The pressure drops because the effect of the decreasing of the delivery pressure is greater than the effect of the gas control Pressure loss initiates . Pressure loss ends . 2970 . The pressure drops because the combustion is affected and the temperature in the combustor descents too. Description of the results for the combustor pressure. Pressure arises due the effect of the gas control valves that treats to keep the charge of the plant by allowing more gas flowrate to the combustor.Low efficiency initiates Low efficiency initiates . Combustor pressure and gas delivery pressure Time period (s) 2790 . 3680 .3500 Low efficiency ends . At loss ends about 3660 s the pressure increases and then descents because the aperture of the gas oscillate due the control algorithm. according Fig.2970 Description of the results for the combustor pressure.Simulation Ends The pressure decreases lightly trying to reach a new (and final) steady state because the gas control valves tend to stabilise their aperture.Gas Turbine Power Plant Modelling for Operation Training 207 6000 5500 5000 4500 1500 1200 900 600 Comb Press Plant Comb Press Sim Delivery Press Sim 300 0 0 600 1200 Delivery Press Plant 4000 3500 1800 2400 3000 3600 4200 Time (s) Fig. Fig.Pressure valves treating to keep the charge.3000 3000 . 23.Low efficiency ends The pressure stabilises. 23 Gas Delivery Pressure (kPa) Combustor Pressure (kPa) . 23 Event Id Nominal charge .Pressure loss initiates 3500 . 3500 .208 Gas Turbines The behaviour of the gas control valves dynamics during the malfunctions transients are explained in table 10. At about 3660 s the gas control valves have a transient because open suddenly but the control detects this abrupt change and limits the valve apertures producing a slight transient in the apertures. The control algorithm allows decreasing the charge and stabilise the apertures and the plant in a new steady state. The gas control valves treat to keep the charge. Gas flowrate and apertures of gas control valves A and C. Description of the results for the fuel gas control valves apertures. The apertures increase their value trying to compensate the charge descending due to the loss of combustion efficiency.2970 2970 . 10 8 6 4 2 0 0 600 1200 1800 2400 3000 3600 Gas Flow Plant Ap Valv A Plant Ap Valv C Plant Gas Flow Sim Ap Valv A Sim Ap Valv C Sim 1.3500 Event Id Description of the results for the fuel gas control valves. The exhaust temperature is measured in the gas phase on the exit of the combustor.0 0. 24. Fig. The changes of the fuel gas flowrate variable for the test are explained in table 11. Valves Aperture(fraction) Fuel Gas Flow (kg/s) .0 4200 Time (s) Fig. The gas control valves adjust their value and control the charge.4200 Pressure loss ends Simulation Ends Table 10.2 0. Time period (s) 2790 .4 0.Low efficiency initiates Low efficiency initiates Low efficiency ends Low efficiency ends Pressure loss initiates The apertures are stable.8 0. 24. according Fig.3680 Pressure loss initiates Pressure loss ends 3680 . Some comments on the behaviour of the exhaust temperature during the malfunctions transients are given in table 12.3000 3000 . 24 Nominal charge .6 0. In Figure 25. 25. At about 3660 s the gas flow has a transient because the valves open and then close (not totally) suddenly.3000 3000 . The gas flow tends to stabilise reflecting the control valves apertures behaviour.3500 3500 . Generated electrical power and exhaust temperature. 24. The graph of the generated electrical power in Figure 25 shows how the charge evolutes depending on the malfunctions. The malfunction is too severe. the generated electrical power is graphed on the left y axis and the exhaust temperature on the right y axis. 200 600 480 360 240 Gen Power Plant Exhaust Temp Plant Gen Power Sim Exhaust Temp Sim 160 120 80 40 0 0 600 1200 1800 2400 3000 3600 120 0 4200 Time (s) Fig. The gas flowrate adjusts its value (grows slightly) according the gas control valves aperture to adjust the charge. The behaviour of the charge is explained in table 13.2970 Event Id Description of the results for the fuel gas flowrate. 2970 . Exhaust Temperature (oC) Generated Power (MW) . 24 Nominal charge . according Fig. The gas flowrate increases following the aperture of the gas control valves trying to compensate the losing of electrical power due the malfunction.4200 Table 11. Description of the results for the fuel gas flowrate. Fig.Gas Turbine Power Plant Modelling for Operation Training 209 Time period (s) 2790 . The gas flowrate descents because the gas control valves are not able to keep the charge.3680 Pressure loss initiates Pressure loss ends Pressure loss ends Simulation Ends 3680 .Low efficiency initiates Low efficiency initiates Low efficiency ends Low efficiency ends Pressure loss initiates The fuel gas flow remains stable. Fig. Time period (s) 2790 . The exhaust temperature arises due the effect of the gas control valves that treats to keep the electrical power by opening and forcing more gas flowrate to the combustor.3500 3500 .4200 Table 13.210 Time period (s) 2790 . Fig.3000 Description of the results for the exhaust temperature. The exhaust temperature decreases tending to stabilise according the gas control valves position. The effect of the malfunction is more important than the effect of the gas control valves.3000 Event Id Gas Turbines Description of the results for the exhaust temperature. The exhaust temperature drops.Low efficiency initiates Low efficiency initiates Low efficiency ends Low efficiency ends Pressure loss initiates The charge is in steady state. 25. according Fig. 25. At about 3660 s the charge oscillates due the gas control valves aperture behaviour. allowing more gas flowrate into the combustor. Description of the results for the fuel gas flowrate. The charge drops because the combustion malfunction and the gas control valves do not compensate the effect that soon. . according Fig.3500 3500 . Description of the results for the fuel gas flowrate.2970 2970 . 25 Nominal charge .4200 Pressure loss ends Simulation Ends Table 12. 3000 . The charge recovers its original nominal value due the control by the gas control valves. The exhaust temperature drops because the combustion is affected and the gas control valves do not respond immediately. The charge tends to stabilise for the steady state defined by the control algorithm.3680 Pressure loss initiates Pressure loss ends 3680 .3680 Pressure loss initiates Pressure loss ends Pressure loss ends Simulation Ends 3680 . At about 3660 s the exhaust temperature has a transient because the gas control valves aperture behaviour.Low efficiency initiates Low efficiency initiates Low efficiency ends Low efficiency ends Pressure loss initiates The exhaust temperature stabilises. 25 Event Id Nominal charge . 3000 .2970 2970 . The charge drops because the malfunction of losing delivery pressure that cannot be nullified by the gas control valves. Acronyms The list of acronyms used in this chapter is: CFE . Now. From the literature review. must be mentioned that all the expected alarms were presented in the precise time.National Centre of Training Ixtapantongo DCS . This simulator had several adjustments during its development to fit its dynamic behaviour to that obtained in the real plant. Presently. and the methodology that supports the development of the simulator. in an important part. training scenarios were defined and used in the simulator to achieve the training program that is probing to be a successful one. 12. The robustness of the models is due. 13. The simulator was tested in all the operation range from cold start to 100% of load and fulfils the performance specified by CENAC including a comparison of its results with plant data. to the generic models approach. high-fidelity. This project was carried out thanks to the financial support of CFE. Conclusion A complete model of a gas turbine generation plant for operators’ training has been presented.Instructor Console ICO . trainers and support personnel of CENAC. Acknowledgment The simulators developed by the SD of the IIE have been projects carried out thanks to the effort. it may be concluded that the present models could be used for other purposes like that reported.Initial Conditions .The National Utility Company in Mexico CENAC .Distributed Control System GM . plant specific simulator for operator training. the CENAC has one more useful tool to train the future generation of operators of the gas turbine power plants. enthusiastic and very professional hard work of researchers and technicians of the IIE as well as very good coordination of the co-operation of operators.Gas Turbine Power Plant Modelling for Operation Training 211 Although they are not presented in this work.Generic Model IC . and with reliable experience in the use of simulators. An additional aspect that gives certitude and robustness to the simulator behaviour is that this has practically the same DCS that the plant which means that the process models that were obtained by the SD engineers reproduce correctly the real behaviour of the reference plant. the software tools. The results demonstrate than the simulator is a replica. considering that the modelling basis of the IIE has less constrains and thus a more wide scope. The CENAC endorsed and accepted as correct the results of the tests in accordance with the testing acceptance procedures. The validation of the simulator was carried out by CENAC specialised personnel under rigorous acceptance simulator testing procedures. Realism is provided by the use of DCS screens emulation. 11. (2001). 20 No. Thailand. Zhang. pp.asp. Epri. A. Vol..Simulation Department SN . E. 1. Dynamic modelling of steam power cycles. 5.Maintenance Node MSS .. Ghadimi. San Antonio..17-19. 223 Part A. Vol.2. Colonna P. 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Y. F. 2nd.H.. 2. Jun 2007. IEEE International conference on power and energy. A. Iki. (2008).214 Gas Turbines Rubechini. Arnone..Y. 021022-1 – 021022-7.. Simplified performance model of gas turbine combined cycle systems.& Cecchi. & Castelloes F. Proceedings of IMECE2008. Frey.Y. Journal of Turbomachinary. Matt.Y. C. Uriu.. 514-519. No. ASME International mechanical Engineering Congress and Exposition. Johor Baharu. pp. Zhu.. Developer of a dynamical model for customer´s gas turbine generator in industrial power systems. Watanabe. Guedes. Massachusetts. Therefore. Gas turbine designers need analytical methods to extrapolate the limited material Xijia Wu . Compressor materials can range from steels to titanium alloys. solidified in the [100] crystallographic direction. 2004). The combination of thermomechanical loads and a hostile environment may induce a multitude of material damages including low-cycle fatigue. creep.. the advances in gas turbine materials are often made through thermomechanical treatments and/or compositional changes to suppress the failure modes found in previous services. the potential failure mechanisms and lifetimes of gas turbine materials are of great concern to the designers. high cycle fatigue. The endurance of the gas turbine engine to high temperature is particularly marked by the creep resistance of HP turbine blade alloy. the methodology of life prediction has been under development for many decades (see reviews by Viswanathan. The early approaches were mainly empirically established through numerous material and component tests. Wu et al. erosive and corrosive attacks. which are composed of intermetallic γ’ (Ni3Al) precipitates in a solution-strengthened γ matrix. low cycle fatigue. given the hostile (hot and corrosive) operating environment. 1. Turbine disc alloys are also mostly polycrystalline Ni-base superalloys. During the service of an aero engine. the traditional approaches are too costly and time-consuming to keep up with the fast pace of product turn-around for commercial competition. The challenges in life prediction for gas turbine components indeed arise due to their severe operating conditions: high mechanical loads and temperatures in a high-speed corrosive/erosive gaseous environment. as the firing temperatures are increased and the operating cycles become more complicated. hot corrosion/oxidation. 2008). National Research Council Canada 1. fretting. 1989. In general. the state-of-the-art turbine blade alloys are single crystal Ni-base superalloys. fretting and oxidation. Coatings are often applied to offer additional protection from thermal. creep. However. Because of its importance. erosion. Nowadays. The cutaway view of an aero engine is shown in Fig. and the hot-section components are mostly considered to be critical components from either safety or maintenance points of view. Introduction The advance of gas turbine engines and the increase in fuel efficiency over the past 50 years relies on the development of high temperature materials with the performance for the intended services. Figure 2 shows the trend of firing temperature and turbine blade alloy capability (Schilke. and thermomechanical fatigue will be induced to the components ranging from fan/compressor sections up front to high pressure (HP) and low pressure (LP) turbine sections at the rear. a multitude of material damage such as foreign object damage. since these materials inevitably incur service-induced degradation.9 Life Prediction of Gas Turbine Materials Institute for Aerospace Research. depending on the cost or weight-saving concerns in land and aero applications. produced by wrought or powder metallurgy processes. 216 Gas Turbines property data. Cutaway view of the Rolls-Royce Trent 900 turbofan engine used on the Airbus A380 family of aircraft (Trent 900 Optimised for the Airbus A380 Family. 1. the requirement of accurate and robust life prediction methods also comes along with the recent trend of prognosis and health management. often generated from laboratory testing. to estimate the component life for the design operating condition. the fundamentals of high temperature deformation are first reviewed. where assessment of component health conditions with respect to the service history and prediction of the remaining useful life are needed in order to support automated mission and maintenance/logistics planning. and the respective constitutive models Fig. Furthermore. Rolls-Royce Plc. Increase of firing temperature with respect to turbine blade alloys development (Schilke. 2. Fig. in this chapter. Derby UK. 2009). 2004). . To establish a physics-based life prediction methodology. whereas the latter process assists dislocation climb and glide within the grain interior. (P) 1 Ideal Material Strength Normalized shear stress. resulting in grain boundary sliding (GBS). T/Tm Fig. the deformation mechanism is understood to be dislocation glide. Dyson & McLean (2000). Elastic (E) and rate-independent plasticity (P) usually happens at low temperatures (i.e. Then. deformation regimes can be summarized by a deformation map. Walker (1981). the evolution of material life by a combination of damage mechanisms is discussed with respect to general thermomechanical loading. power law breakdown ) ε Elasticity GBS ε 1 0 Homologous temperature. These constitutive models . shearing or looping around the obstacles along the path. crack growth problems and the damage tolerance approach are also discussed with the application of fracture mechanics principles. 2. A schematic deformation mechanism map. for a polycrystalline material. where Tm is the melting temperature). and the material failure mechanism mainly occurs by alternating slip and slip reversal.Life Prediction of Gas Turbine Materials 217 are introduced. resulting in intragranular deformation (ID) such as the power-law and power-law-breakdown.g. The former process assists dislocation climb and glide along grain boundaries.3 Tm. e. following Frost and Ashby (Frost & Ashby. T < 0. 1982). as shown schematically in Fig. Furthermore. and most recently. ln(σ/G) Dislocation Glide (ID) Dislocation Creep (power law . dislocations are freed by vacancy diffusion to get around the obstacles so that time-dependent deformation manifests. several unified constitutive laws have been proposed. leading to fatigue. 3. 3. As temperature increases. Fundamentals of high temperature deformation In general. except for ultimate tensile fracture and brittle fracture. In an attempt to describe inelastic deformation over the entire stress-temperature field. Chaboche & Gailetaud (1986). In the plasticity regime. Time dependent deformation at elevated temperatures is basically assisted by two diffusion processes—grain boundary diffusion and lattice diffusion. with the associated deformation mechanisms is the foundation for the development of an integrated creep-fatigue (ICF) modelling framework as outlined in the following sections (Wu et al. a back stress may arise from competition between work hardening (dislocation pile-up and network formation) and recovery (dislocation climb) as: . Note that the stress and temperature dependence of the plastic multiplier is described by a hyperbolic sine function. we proceed with the basic concept of strain decomposition that the total inelastic strain in a polycrystalline material can be considered to consist of intragranular strain εg and grain boundary sliding εgbs. (1). (3) covers both the power-law and the power-law-breakdown regimes in Fig. 1994). and hence have limitations in correlating with the transgranular. and T is the absolute temperature in Kelvin. In keeping consistency with the Prandtl-Reuss-Drucker theory of plasticity. M is a dislocation multiplication factor. (3). the rate of the net dislocation movement can be formulated as a hyperbolic sine function of the applied stress (Wu & Krausz. as: ε in = ε g + ε gbs (1) The physics-based strain decomposition rule. a physics-based theoretical framework encompassing the above deformation and damage mechanisms is needed. overcoming the energy barriers of the lattice. k is the Boltzmann constant. with the evolution of activation energy ψ given by: ψ= V eq σg kT (5) where V is the activation volume. As intragranular deformation proceeds.218 Gas Turbines employ a set of evolution rules for kinematic and isotropic hardening to describe the total viscoplastic response of the material. which may occur by glide at low temperatures and climb plus glide at high temperatures. but do not necessarily differentiate whether the contribution comes from intrgranular deformation mechanism or GBS. 2. in tensor form. can be expressed as ε g = pg n g where p g is the plastic multiplier as defined by (2) p g = 2 A(1 + Mp g )sinh (ψ ) = 2 ε g : ε g 3 (3) where A is an Arrhenius-type rate constant. Eq. 2009). By the theory of deformation kinetics (Krausz & Eyring. the flow rule of intragranular strain. Eq. Eq. Therefore. To that end.1 Intragranular deformation Intragranular deformation can be viewed as dislocation motion. 1975). and ng is the flow direction as defined by ng = 3 (s − χ g ) eq 2 σg (4) where s is the deviatoric stress tensor and χg is the back stress tensor. intergranular and/or mixed failure modes that commonly occur in gas turbine components. 3. but to keep the simplicity for small-scale deformation (<1%). The GBS flow direction is defined by n gbs = 3 s − χ gbs eq 2 σ gbs ( ) (10) The two equivalent stresses in Eq.2 Grain boundary sliding Based on the grain boundary dislocation glide-climb mechanism in the presence of grain boundary precipitates (Wu & Koul. 1995) . l is the grain boundary precipitate spacing. r is the grain boundary precipitate size. as demonstrated in the later examples. (6) is suffice. (9) are given by eq σ gbs = 3 s − χ gbs : s − χ gbs 2 ( )( ) (11) and σ eq = 3 s:s 2 (12) The evolution of the grain boundary back stress in the presence of grain boundary precipitates is given by (Wu & Koul. and b is the Burgers vector. Note that more complicated expressions that consider both hardening and dynamic/static recovery terms may need to be used to formulate the back stress with large deformation and microstructural changes. 1995. and q is the index of grain boundary precipitate distribution morphology (q = 1 for clean boundary. q =2 for discrete distribution.Life Prediction of Gas Turbine Materials 219 χg = 2 H gε g − κ χ g 3 (6) where Hg is the work-hardening coefficient and κ is the climb rate (see detailed formulation later). the governing flow equation for GBS can be expressed as ε gbs = pgbsngbs with a GBS multiplier as defined by pgbs = φ Dμb ⎛ b ⎞ ⎛ l + r ⎞ kT ⎜ d ⎟ ⎜ b ⎟ ⎝ ⎠ ⎝ ⎠ q q −1 (8) ( σ )( σ eq gbs eq 2 − σ ic ) μ (9) where D is the diffusion constant. eq σg = ( )( ) (7) 2. 1997). μ is the shear modulus. d is the grain size. The effective equivalent stress for intragranular deformation is given by 3 s − χg : s − χg 2 where the column (:) signifies tensor contraction. and q = 3 for a network distribution). Eq. By solving all the components of inelasticity. inevitably leading to crack nucleation. The back stress formulation. σic. (9). once it surpass a threshold stress. To describe the process of cyclic deformation. the evolution of the stress tensor is governed by σ = C : (ε − ε in ) (16) 3. controls grain boundary dislocation climb. and their morphology. Deformation processes and constitutive models 3. controls the grain boundary dislocation glide with a back stress χgbs. the grain boundary precipitate size and spacing. and recovery by dislocation climb. when intersecting at the interface of material discontinuities (surface. For uniaxial strain-controlled loading. Eq. states the competition between dislocation glide.) result in intrusions/extrusions or dislocation pile-ups. σ gbs . (9) depicts the grain boundary plastic flow as a result of dislocation climb plus glide overcoming the microstructural obstacles present at the grain boundaries. 1997): 2 ⎧ -1 ⎪ 2 ⎪ 1 + ⎛ 2h ⎞ ⎜ λ ⎟ ⎪ ⎝ ⎠ ⎪ φ=⎨ 2 ⎪ -1 2 ⎪ ⎛ πh ⎞ ⎪ 1+⎜ ⎟ ⎪ ⎝ λ ⎠ ⎩ for trianglular boundaries (15) for sinusoidal boundaries where λ is wavelength and h is the amplitude. as given by the factor φ (Wu & Koul. σ eq . The other equivalent stress. grain boundaries or inclusions. the deformation is constrained as: ε= σ + ε p = constant Ε (17) .1 Cyclic deformation and fatigue It is commonly known that a metal subjected to repetitive or flunctuating stress will fail at a stress much lower than its ultimate strength. As shown in Eq. (13). etc.220 Gas Turbines χ gbs = 2 H gbsε gbs − κχ gbs 3 (13) where Hgbs is the grain boundary work hardening coefficient. leading to formation of persistent slip bands (PBS) and a dislocation network in the material. that arises from the constraint of grain boundary precipitates. Eq. Henceforth. we start with tensile deformation as follows. The underlying mechanisms of fatigue is dislocation glide. Last but not least. Persistent slip bands. and κ is the dislocation climb rate as given by κ= eq Dμb ( σ − σ ic ) kT μ (14) eq The equivalent stress for GBS. GBS is also affected by the grain boundary waveform. Failures occuring under cyclic loading are generally termed fatigue. the GBS multiplier is controlled by the grain boundary diffusion constant D and grain boundary microstructural features such as the grain size. which causes grain boundary dislocation pile-up. . we have the first-order differential equation of Ψ. (20). b = 1 + χ2 + 1 (20) The initial time of plastic deformation is defined by Ψ0 = (σ − Hε 0 − σ 0 ) p kT =0 (21) where ε0p is the plastic strain accumulated from the prior deformation history. as (Wu et al. It is applicable to high strain rate loading conditions. as an integration constant.e. Eq. plasticity commences. Once the stress exceeds the initial lattice resistance in the material. Eq. i.. In this sense. in comparison with the . which are often encountered during engine start-up and shutdown or vibration conditions caused by mechanical and/or aerodynamic forces. a = ε ⎝ E⎠ 1 + χ2 − 1 χ . M = 0). From Eq. and σ0. At the first loading. represents the initial lattice resistance to dislocation glide.e. As an example. (22) and shown in Fig. Based on the deformation kinetics. (17) (neglecting dislocation climb. and multiplication. (21). 4. σ0 corresponds to the critial resolved shear stress by a Taylor factor. i.Life Prediction of Gas Turbine Materials 221 Substituting Eq. ω(ε) is a response function as defined by ⎧ V(Eε − σ ) 1 + χ 2 ⎫ ⎛ 1−a ⎞ ⎪ ⎪ 0 ω(ε) = ⎜ ⎜ ⎟ exp ⎨ − ⎬ χ +b⎟ kT ⎝ ⎠ ⎪ ⎪ ⎩ ⎭ (23) Eq.e. (22) basically describes the accumulation of plastic strain via the linear strain-hardening rule with dislocation glide as the dominant process and limited dislocation climb activities.. (22) describes the time and temperature dependence of high temperature deformation. σ > σ0. then t0 =σ0/(E ε ). we can obtain the stress-strain response as follows: σ − Hε p − σ 0 = − kT ⎛ a + ω(ε )b ⎞ ln ⎜ ⎟ V ⎜ 1 − ω(ε ) χ ⎟ ⎝ ⎠ (22) where. ε0p = 0.. 850 oC and 950 oC are described using Eq. (3-7) into Eq. Since the deformation is purely elastic before the condition. i. the tensile behaviors of IN738LC at 750 oC. 2001) Ψ= which can be solved as EV kT ⎡ ⎤ H⎞ ⎛ ⎢ ε − 2 A ⎜ 1 + ⎟ sinh Ψ ⎥ E⎠ ⎝ ⎣ ⎦ (18) 2 ⎫ ⎧ ⎛ e −Ψ − a ⎞ ⎛ 1 − a ⎞ ⎪ VEε(t − t0 ) 1 + χ ⎪ ⎜ −Ψ ⎟=⎜ ⎟ exp ⎨− ⎬ ⎜ χe + b ⎟ ⎜ χ + b ⎟ kT ⎠ ⎪ ⎪ ⎝ ⎠ ⎝ ⎩ ⎭ (19) where χ= 2A ⎛ H⎞ ⎜1 + ⎟ . κχ g << Hε . is met: σ = E ε t. 01 Strain (mm/mm) 0.222 Gas Turbines experimental data.005 -5 -1 750 C 0 850 C 0 950 C 0 IN738LC Strain Rate: 2x10 sec 0.950 0 C 500 400 Stress (MPa) 300 200 100 2x10 -3 sec -1 2x10 -4 sec -1 2x10 -5 sec -1 Model 0 0 0. 5.005 0. 600 IN738LC .01 Strain (m m/mm ) 0. Stress-strain curves for the IN738LC with the lines as described by Eq.015 Fig. Stress-strain responses of IN738LC to different loading strain rates at 950 oC. The strain rate dependence of the tensile behavior of this alloy at 950oC is also demonstrated in Fig. The parameters for this material model are given in Table 1. (22). 5. 900 800 700 600 Stress (MPa) 500 400 300 200 100 0 0 0.015 Fig. . 4. material deforms purely elastically when the stress is below σ0. As far as deformation in a lifing process is concerned. let us examine the cyclic deformation process as follows. H (MPa/mm/mm) Modulus of Elasticity. (22). except in the transition region from the elastic to the steady-state plastic regimes. The solid line represents the model prediction with the parameters given in Table 1 (except σ0 = 40 MPa for this coarser grained material). Constitutive Model Parameters for IN738LC This constitutive model has 6 parameters: E.977x10-22 0. the work-hardening coefficient. Eq. σ0 (MPa) Work Hardening Coefficient. σ0. But before that. which have defined physical meanings. even though the macroscopic behaviour still appears to be in the elastic regime. (22) describes the monotonic loading up to a specified strain.38×10-19 Table 1.5x10-7 3. which may still be well below the engineering yield surface defined at 0. the hysteresis loop of IN738LC is shown in Fig. (22) implies. but plasticity starts to accumulate just above that. This process repeats as the cycling proceeds. A0 (sec-1) Activation Energy. ΔG0≠ (J) 750 540 15000 175. A0 and ΔG0≠. 1981) have given a theoretical treatment for fatigue crack nucleation in terms of dislocation pile-ups. b) interstitial dipole which leads to extrusion.56x10-7 950 110 12478 137. are constants corresponding to a “constant microstructure”. first. just by analyzing the tensile behaviour with Eq. 7 shows a schematic of crack nucleation by a) vacancy dipole.5x10-8 850 285 13736 151. σ0 may correspond well to the fatigue endurance limit. the description is mostly suffice. E (GPa) Strain-Rate Constant. which leads to intrusion.7 2. A = A0exp[-ΔG0≠/kT] (sec-1) Activation Constants Activation Volume. The activation parameters. The model prediction is in very good agreement with the experimental data.4 1. The present model. (22). Tanaka and Mura (Tanaka & Mura. which usually occurs within a small deformation range of ±1%. The significance will be further discussed later when dealing with fatigue life prediction. Fig. 6. Upon load reversal at the maximum stress point. In this sense. The elastic modulus. the material has 2σ0 + Hεp as the total stress barrier to yield in the reverse cycle. also incorporates some microstructural effects via H and σ0. or c) tripole that corresponds to an intrusion-extrusion pair. which may be attributed to the model being calibrated to a finer-grained material. one may obtain an important parameter for fatigue life prediction. A0 and ΔG0≠. As an example.2% offset. This means that the commencing of plastic flow may first occur at the microstructural level. are temperature-dependent. in the context of Eq.0 5. V (m3) Pre-exponential. V.5 3. H and the initial activation stress σ0.Life Prediction of Gas Turbine Materials 223 Temperature (ºC) Initial lattice resistance. Under isothermal fully-reversed loading conditions. They obtained the following crack nucleation formula: . Therefore. V. E. H. As Eq. Eq. Dislocation pile-ups by (a) vacancy dipoles (intrusion).005 Experiment Predicted IN738LC 0 Temperature: 950-5C -1 Strain Rate: 2x10 sec -0.0025 0 0. 6.0025 Mechanical Strain (mm/mm) 0. Hysteresis loop of IN738LC at 950oC.005 Fig. Δεp = Δε . 7. Nc = 4(1 − ν )ws 1 μb Δγ 2 (24) where Δγ is the plastic shear strain range.224 Gas Turbines 200 150 100 Stress (MPa) 50 0 -50 -100 -150 -200 -0. (24) can also be written in the following form: 1 Δσ ⎞ ⎛ 2 = Cε p = C ⎜ Δε − N E ⎟ ⎝ ⎠ 2 (25) . Under strain-controlled cycling conditions.Δσ/E. (a) vacancy dipole (b) interstitial dipole (c) tripole Fig. (b) interstitial dipoles (extrusion) and (c) tripoles (intrusion-extrusion pair). the local deformation behaviour is leaning more towards strain-controlled condition. in comparison with the experimental data (Fleury & Ha. are used for the evaluation.009 for fully-reversed low cycle fatigue of IN738 at 400oC. 8 shows the prediction of Eq. Eq. as listed in Table 1. since it is believed that with the constraint of the surrounding elastic material. 2001). 400 C. When the fatigue life is correlated with the total strain range. LCF life of IN738 in terms of plastic and total strain (%). The flow stress σ is obtained from Eq. when the fatigue life is correlated with the plastic strain range. 8. (25) with C = 0. Apparently. the relationship becomes nonlinear. according to Eq. IN738LC 10 LCF. the predicted endurance limit σ0/E is approximately 0. as established by Coffin (1954) and Mansion (1954). 400 C.1 10 100 1000 10000 100000 0.4. To establish the relationship. failure cycles less than 104 has been termed low cycle fatigue (LCF). (22). As shown in Fig. the relationship is represented by a straight line in the log-log scale. and also stress controlled cyclic tests when plasticity is not measurable.01 num ber of cycles to failure Fig. In this case. the material properties at 750oC.Life Prediction of Gas Turbine Materials 225 Fig. (25). Since the tensile behaviour of IN738 exhibits no significant temperature dependence below 700oC. b. 8. total s train LCF. which agrees well with the experimental observation. ε′f and σ′f are empirical constants. and above that high cycle fatigue (HCF). plas tic s train 1 strain range 0. the material’s fatigue life approaches infinity when the total strain ε → σ0/E. whereas HCF data are usually used to . Arbitrarily. (26) has been extensively used by engineers analyzing fatigue data. one needs to conduct strain-controlled cyclic tests with appreciable plastic deformation. Laboratory LCF data are usually used to estimate the life of component with stress concentration features such as notches and holes. through numerous experimental observations on metals and alloys. The nonlinear total-strain-based fatigue life equation is often written as: Δε p = ε′f N c + f σ ′f E Nb f (26) where c. which can have a severer impact . HCF failures are usually associated with vibration-induced stresses due to mistune or other geometrical damage that change the vibration characteristics of the component. an LCF cycle may represent major loading cycles such as engine start up -shutdown. (25) can be used for both LCF and HCF regimes with the material constitutive law. occurs under low-amplitude cyclic stresses where deformation is primarily elastic. on the other hand. Eq.226 Gas Turbines assess the component life under elastic stresses. 2009a). Fig. (28). HCF. During engine start up and shutdown.2 Thermomechanical fatigue Advanced turbine blades and vanes often employ a sophisticated cooling scheme. it has been show that Eq. (22). 3. and hence exhaust its fatigue life after a short period of time. (25) can be rewritten as σ = σ 0 + H(BN)−1 / 2 (28) Fig. S-N curves of Ti6Al4V under pristine and foreign object damaged conditions (Wu. When the applied stress is well below the engineering yield point. these components experience thermal-mechanical cyclic loads. Eq. 9. It can potentially simplify the fatigue analysis by calibrating with a few cyclic tests in either LCF or HCF regime. For gas turbine engine components. It can become a life-threatening mode of failure especially when it is superimposed on LCF induced cracks. the logarithm term in Eq. Under these conditions. in order to survive at high firing temperatures. components vibrate with high frequencies that can reach thousands of cycles per second. In summary. (22) is nearly zero such that the plastic strain can be approximated by εp ≈ σ − σ0 H (27) and Eq. 9 shows the S-N relationship of Ti-6Al-4V described with Eq. (25) can also be extrapolated to HCF under stress controlled fatigue conditions. as schematically shown in Fig. which has a phase angle in between. A more sophisticated engine cycle is shown in Fig. ii) the out-ofphase (OP) cycle. and a hold period at the maximum load. which has a 180o phase angle.2 1 0. Temperature-strain cycles for different TMF tests. usually simple TMF cycles are employed: i) the in-phase (IP) cycle.6 0.6 te mpe ra ture 0.Life Prediction of Gas Turbine Materials 227 on the life of the material than isothermal conditions. Strain OP DP IP Tmin Tmax Temperature Fig. which consists of a half diamond-phase cycle. 11. a thermal excursion from Tmean to Tmax.8 engine speed 0. 10. and iii) the diamond phase (DP) cycle.8 1 1. An engine TMF cycle. For laboratory studies. Engine TMF Cycle 1. 11. The OP and IP cycles represent two extreme conditions. .2 0.2 0 0 0. where the maximum stress is reached at the “hot” end of IP and the “cold” end of OP temperature cycle.2 Fig. 10. Thermomechanical fatigue (TMF) refers to the fatigue behaviour of a material under simultaneously thermal and mechanical loads.4 0.4 Startup Shut down 0. which has a 0o phase angle between thermal and mechanical loads. physics based models are needed to describe the complex damage processes under TMF loading. for plastic flow to commence. oxidation and creep in some combination. The damage accumulation and interactions during TMF can be very complex. Many factors such as the maximum and minimum temperature. However. After mathematical rearrangement. (18) can be integrated into the form: ⎛ e −Ψ − a ⎞ VEε 1 + χ 2 ln ⎜ −Ψ Δti =− ⎟ ⎜ χe + b ⎟ kTi ⎝ ⎠ Ψ i −1 Summing up all these infinitesimal steps. It is almost a formidable task to characterize these effects completely by experimental approaches such as those adopted for LCF and HCF assessments. as defined by Eq. or in other words. T is the current temperature.2. Interactions with oxidation and creep under general TMF conditions will be discussed later. the combined effects of temperature and stress could just induce one dominant damage mode. Ψ. and environment can all influence TMF life. for example. and the right-hand side is an integration of the temperature-dependent terms over the loading period.228 Gas Turbines During TMF. T0 is the reference temperature. and α is the thermal expansion coefficient. (31) will be equal to the logarithmic difference between the final state and the initial state. undergoes a series of infinitesimal isothermal steps. For TMF. for each i-th step. the total strain (εtot) is the sum of thermal and mechanical strain components: εtot = εth + εmech = α (T − T0 ) + εmech (29) where εth is the thermal strain. In this section. the combined damage mechanisms and their interactions can be complicated. Eq. Therefore. it is generally believed that the IP cycle produces predominantly creep damage. because it usually involves fatigue. we assume that the evolution of the energy. In extreme cases. the cyclic thermomechanical deformation behaviour is described. The mechanical strain (εmech) in general can be considered as the sum of the elastic and inelastic strain components. thermal and mechanical strain ranges. under general TMF conditions. we have: N ⎛ e −Ψ − a ⎞ VEε 1 + χ 2 Δti ∑ ln ⎜ χ e−Ψ + b ⎟ = − ∑ kT ⎜ ⎟ i i =1 i =1 ⎝ ⎠ Ψ i −1 N Ψi (i=1. the left-hand side of Eq. we have: ⎧ t V μγ 1 + χ 2 ⎫ ⎛ e −Ψ − a ⎞ ⎛ 1 − a ⎞ ⎪ ⎪ = dt ⎬ exp ⎨ − ∫ ⎜ −Ψ ⎜ χe + b ⎟ ⎜ χ + b ⎟ ⎟ kT ⎠ ⎪ ⎪ ⎝ ⎠ ⎝ ⎩ t0 ⎭ (32) where t0 is the time to reach the elastic limit. the strain rate. Let . the phasing between temperature and strain.…) (30) Ψi (31) Let N→∞. Then. 1992). the energy state evolves from Ψi-1 to Ψi over the time interval Δti = ti –ti-1 at a constant temperature Ti. dwell time. while the OP cycle induces oxide-scale cracking (Sehitoglu. (21). 12. respectively. the variation of E is moderate such that it can be represented by its average Em. The predicted hysteresis loop is in good agreement with the experimentally measured response.e. Then. 500 400 300 Stress (MPa) 200 100 0 -100 -200 -300 Experiment Predicted -0. (22).ε relationship. the -/+ sign is used for the temperature rising or declining halves of the cycle. similar to Eq. the T .10.0025 0 0. and T0 denotes the temperature point at which the stress reaches the elastic limit.005 -0.OP TMF 0 Temperature: 750-950 C -5 -1 Strain Rate: 2x10 sec Fig. Stress-strain response of IN738LC (coarse-grain) during an OP-TMF cycle. ω =⎜ ⎧ VE Δε 1 + χ 2 ⎛ 1−a ⎞ T⎫ ⎪ ⎪ m ln ⎬ ⎟ exp ⎨∓ χ +b⎠ kΔT T0 ⎪ ⎝ ⎪ ⎩ ⎭ (34) where ΔT = Tmax . as shown in Figure 2.005 IN738LC . . Δε is the total strain range. (35). (32) can be rewritten into the stress vs. i. which can be determined based on the thermomechanical cycle profile.1 but with a reduced σ0 =40MPa for the coarsegrained (d~5mm) material.Life Prediction of Gas Turbine Materials 229 ω (t ) = ⎜ ⎧ t VEε 1 + χ 2 ⎫ ⎛ 1−a ⎞ ⎪ ⎪ dt ⎬ ⎟ exp ⎨− ∫ kT ⎝ χ +b⎠ ⎪ t0 ⎪ ⎩ ⎭ (33) and assume that within the temperature range of TMF.. as σ − Hε p − σ 0 = − kT ⎛ a + ωb ⎞ ln ⎜ ⎟ V ⎝ 1 − ωχ ⎠ (35) The stress-strain response of the coarse-grained IN738LC under an out-of-phase thermomechanical fatigue condition is predicted using Eq. the ω function can be evaluated as. and 1 + χ 2 ≈ 1 since χ is usually small.0025 Strain (mm/mm) 0. Eq. with the parameter values given in Table 2. strain function.Tmin is the temperature range. and concluded that grain boundary sliding is primarily responsible for the transient creep behaviour. creep damage assessment has been mainly based on the minimum creep rate and the Larson-Miller plot. It is generally understood that the creep rate has different stress dependence by different mechanisms. It has been known that creep deformation is a continuous physical process. (8)-(14) has the form (Wu & Koul. the solution of Eq. 1982. 1995) ε gbs = ε 0 + φε sst + σ β 2H gbs ⎡ ⎛ β 2φ H gbsε sst ⎞ ⎤ ⎢1 . Traditionally. Ashby & Dyson. based on the decomposition of the total inelastic strain into grain boundary sliding and intragranular deformation. Creep mechanisms have been extensively reviewed (Frost & Ashby. For component life prediction. R is the universal gas constant. In gas turbine engines. and A0 and n are empirical constants. (36).exp ⎜ ⎟⎥ ⎜ σ ( β . the steady-state creep rate (or the minimum creep rate) is often expressed in a Norton-Bailey form. the stress vs.1) ⎟ ⎥ ⎢ ⎝ ⎠⎦ ⎣ (37) where β is a microstructure parameter. Creep can be one of the critical factors determining the integrity of components at elevated temperatures. Wu & Koul. (1). 13 shows the Larson-Miller plot for Astroloy. 1985. as ⎛ Q ⎞ n ε = A0 exp ⎜ ⎟σ ⎝ RT ⎠ (36) where Q is the activation energy. Nevertheless. it needs a constitutive law of creep to describe the stress relaxation and redistribution with time as creep deformation proceeds.3 Tm (Tm is the material’s melting point). In general. components such as turbine blades are subjected to sustained loads (centrifugal force and pressure) at high temperatures during the operation. usually above 0. especially in hot sections. Wu & Koul (1996) have proposed a creep-curve model. creep damage may interact with fatigue that leads to significant reduction in the service life of the component. it is merely an experimental correlation rather than a physics-based model. where a decreasing creep rate regime (transient creep: primary plus secondary) is followed by an accelerating creep rate regime (tertiary creep) beyond a minimum creep rate. Under uniaxial loading condition. as expressed in Eq. Larson-Miller parameter relationship is nonlinear due to the multiple creep mechanisms involved. 1996).230 Gas Turbines 3. and therefore. Furthermore. Fig. Creep of a turbine blade can also cause dimensional changes that either reduce its aerodynamic efficiency or lead to elongation that rubs the engine casing. T is the absolute temperature. Extrapolation to predict the long term creep life using LarsonMiller parameter has to be based on extensive testing. taking into consideration the temperature compensated rate property as exhibited in Eq. which may induce additional vibration and noise.3 Creep Creep is a mode of inelastic material deformation occurring under sustained loading at high temperatures. and ε ss = φ(1 − β −1 ) Dμb ⎛ b ⎞ ⎛ l + r ⎞ kT ⎜ d ⎟ ⎜ b ⎟ ⎝ ⎠ ⎝ ⎠ q q −1 σ ( σ − σ ic ) μ2 (38) . while the tertiary creep evolves mostly intragranular deformation with dislocation multiplication. Life Prediction of Gas Turbine Materials 231 Fig. First of all. such as dislocation multiplication. the true steady-state creep occurs at a rate as described by Eq. Tertiary creep phenomena will be discussed later. which defines the primary time as follows. as defined by ε tr = p σ β H gbs 2 (39) It states that the primary strain is proportional to the applied stress σ divided by the work hardening coefficient Hgbs. we will discuss the important characteristics of transient creep before the commencing of tertiary creep. It is influenced mostly by grain boundary microstructure and morphology. thus emphasizing the importance of grain boundary engineering in alloy design.6. These processes may eventually take over and lead to an acceleration in the creep rate. However. 13. According to Eq. Equation (37-38) is derived from the grain boundary dislocation glide plus climb mechanism. which is controlled by damage accumulation in both grain interior and along grain boundaries. Presently. . The Larson –Miller plot for Astroloy. (37). since the primary strain is reached as an exponential function of time. It states that the transient creep is a grain boundary sliding phenomenon that consists of a primary stage and a steady-state stage. the primary strain can be attained ~99 percent when the exponential term reaches 4. This relationship may provide guidance for grain boundary engineering to lower the primary strain in alloy applications. Practically. a quasi-steady-state may be observed relatively soon after creep deformation starts. precipitate coarsening and cavity nucleation and growth. the present model predicts a primary strain. Practically. how long the quasisteady-state will last depends on the time to the onset of tertiary creep. (38) only after an infinitely long time. as shown in Fig. the apparent stress dependence may change since the presence of grain boundary precipitates can induce a back stress. It should be noted that Eq. Material Condition New 14159 hrs. The descriptions have been made using Eq. The minimum creep rate correlation for Nimonic 115 (Wu and Koul. creep curves of Alloy 718 and IN738 with planar and wavy grain boundaries are shown in Fig.1 0. Fig. (37) in its present form does not include a damage parameter. 15 shows the creep curves obtained using Eq.. (15). σic. (37) with the parameters as given in Table 2. The creep data generated by Castillo et al. (37-38).313 1. (38). Fig. given in Table 3. (37) with the microstructure parameter and the wave factor φ.45 β 1. 17. However.0 ε m (10-9 s-1) 2.1)σ β 2H ε m (40) Second of all. 14. 16 and Fig. the present model predicts that ideally the GBS strain rate has a stressdependence to the 2nd power.05 Table 2.0 3.232 Gas Turbines t tr = 4. creep data on Nimonic 115 (Furrillo et al. 1995).0 30. Eq.13 H (GPa) 18. 1979) can be correlated with Eq. respectively. The coupling of GBS with grain boundary cavitation and/or oxidation will be discussed later. Creep Curve Parameters for IN738LC under Stress of 90MPa .6 p ( β . For example. In addition. and therefore only applicable to the point before tertiary creep commences. Test Temperature 954 oC 954 oC ε0 (%) 0. 14. (1988) on new and service exposed IN738LC turbine blade materials have also been analyzed with Eq. 6 1.78 φ 1. 1996): ε g = (1 + Mε g )ε i (41) .00233 204.5 1. 15.38 0. This means that the primary creep mechanism of intragranular deformation is negligible. Materials & Test Conditions Alloy 718 σ = 590 MPa T = 650 oC IN738LC σ = 586 MPa T = 760 oC Grain Boundary (planar) h=0 λ=d (triangular) h = 2 μm λ = 10 μm (planar) h=0 λ=d (sinusoidal) h = 5 μm λ = 15 μm H (GPa) 204. (2)-(7) that at constant stress.13 0. it is reasonable to assume that during constant-stress creep. 1978).0 ε m (hr-1) 0. (37) (Wu & Koul.00168 106.Life Prediction of Gas Turbine Materials 233 Fig. a steady-state of back stress is attained soon upon loading such that the intragranular strain rate ε i =const.5 1. It can be inferred from Eq. Creep curves of new and service-exposed IN738LC as predicted by Eq.72 0. 1995).0397 106. which is often the case as observed in single crystal materials (Carry & Strudel.78 0. The tertiary creep strain then may accumulate with dislocation climb and multiplication as (Wu & Koul.0 0.0152 Table 3.13 1. Thus.6 β 1. 1977. deformation would stop by work-hardening due to pile-up of gliding dislocations unless dislocation climb helps the dislocations to bypass the obstacle. Microstructure and Creep Curve Parameters of Alloy 718 Intragranular deformation has been discussed in the previous section. Creep curves of IN738LC with planar and sinusoidal wave grain boundaries. 1997). adding the strain contributions from Eq. as predicted by Eq.234 Gas Turbines Fig. (1). The integration of Eq (41) leads to the following strain-time relation: εg = 1 [exp( Mε i t ) − 1] M (42) Then. 16.1) ⎟ ⎥ M ⎟ ⎢ ⎝ ⎠⎦ ⎣ (43) . we obtain the total creep strain as ε = ε 0 + φ ε sst + σ β 2H ⎡ ⎛ β 2φ H ε sst ⎞ ⎤ 1 [exp( Mε it ) − 1] ⎢ 1 . Fig. according to Eq. (37) (Wu & Koul. where M is the normalized dislocation multiplication factor.exp ⎜ ⎥ ⎜ σ ( β . 1997). (37) (Wu & Koul. (37) and (42) together. 17. Creep curves of Alloy 718 with planar and triangular wave grain boundaries. as predicted by Eq. but grain boundary damage may still occur under stress. 18. as shown in Fig. Wu & Koul (1996) have summarized the grain boundary damage accumulation processes via cavitation and oxidation. intragranular deformation may overshadow GBS by the mere amount of strain accumulation. 18. 1996). The grain boundary wave factor φ for the MHT material is 0. As a first approximation. (43) (Wu & Koul. and the rupture time is reached at ω = ωcr. we assume a constant cavity density and only consider the growth of these cavities. (43). During tertiary creep. 1975): Α(t ) = ρc (t )π rc2 + 2π ∫∫ r(t − ζ )r(t − ζ )ρc (τ )dζ dτ 0τ t t (44) where rc is the critical nucleation radius. ρc(t) is the void density and r(t) is the cavity radius at time t. as indeed most creep rupture occurs intergranularly in polycrystalline materials.7 with h = 2 μm and λ = 10 μm (Table 3). The creep behaviour of wrought Alloy 718 with planar (the SHT material) and triangular-wave (the MHT material) grain boundaries at 650 °C under stress of 593 MPa were reported (Chang et al. 19. the cavity growth rate is approximately equal to r = ε ss d (note that it is the GBS deformation component that dominates the steady-state creep rate in this case). The average rupture time of the SHT material was 450 hours. the creep life of the . as predicted by Eq. 1992). which limits the creep rupture life.0035 h-1. the results are shown in Fig. The agreement with experimental observation is corroborated with the physical rationale that the two IN738LC materials have nearly the same intragranular microstructure in terms of γ′ precipitate size and volume fraction but different grain boundary morphology. Creep curves for IN738LC with planar and serrated grain boundaries. Fig.. Based on the above consideration.3 and ε i = 0. then tr ∝ 1/ ε ss .Life Prediction of Gas Turbine Materials 235 Using Eq. Continuous cavity nucleation and growth has been described by (Raj & Ashby. If we define the creep damage parameter as ω = A/πd2. the creep behaviour of IN738LC with and without grain boundary serration are re-analyzed with additional parameters M = 14. This proves that indeed the transient creep and creep life is limited by GBS. when the oxide crack reaches a critical length. which implies a GBS phenomenon. Suppose that oxygen penetrate the material inward through a parabolic law until the oxide scale is broken by deformation. (45). and hence it follows the relationship of ε min ∝ 1/d. This observation can be directly translated to the above statement.236 Gas Turbines MHT material is estimated to be trMHT = trSHT/φ = 642 hours under the given test condition. Sessions et al. 20. Creep curves for standard and damage tolerant microstructures of Alloy 718 (Chang et al. Fig. 20. as predicted by Eq. Another mechanism for grain boundary damage is gaseous environmental attack—normally at high temperatures—oxidation. then Eq. but the life is inversely proportional to √d. (1977) studied the creep-oxidation interaction in Udimet 700. the rupture time decreases with the number of grains per cross-section with a power of -1/2. we would expect that tr ∝ √d. Suppose that GBS occur at nearly a constant rate for most of the material’s creep life. (45) would lead to tr ∝1/√ ε min . 19. we can see that the creep rate in air increases and the rupture time decreases with the number of grains per cross-section. In Fig. the rate of oxide cracking can be expressed as dx dt ⎛ 2 Dε gbs =⎜ ⎜ ε* ⎝ ⎞2 ⎟ ⎟ ⎠ 1 (45) ox where x is the oxide crack length. By re-plotting their data on the log-log scale as shown in Fig. which is very close to the experimental observation. and ε* is the fracture strain of the oxide. 1992). The air-tested creep rate increases linearly with the number of grains per cross section. considering that the number of grains per cross-section is inversely proportional to the grain . D is a diffusion constant. Therefore. . in air and vacuum. Therefore. (a) (b) Fig. (a) Minimum creep rate data and (b) rupture life data for Udimet 700 at 927°C and 172 MPa. (45) is suitable for describing the oxidation damage during creep.Life Prediction of Gas Turbine Materials 237 size d for fixed specimen geometry. 20. Eq. with the parameters given in Table 4. and T is the absolute temperature. the applied stress and temperature. The majority of the creep life of DS and SX Nibase superalloys is spent in the tertiary stage with a creep ductility in the order of 20~30%. (42) is appropriate to describe the creep behaviour of such alloys. Eq. Eq. Therefore. depending on the material’s microstructure. on the other hand. One creep curve was calculated to predict the creep rupture response at 186MPa/982oC with an observed life of 120 hr. Eq.. the total creep strain is equal to the sum of intragranular strain and GBS strain. by the deformation decomposition rule. ignore grain boundary sliding (GBS) from Eq. Eq.238 Gas Turbines To overcome the weakness of grain boundaries which are susceptible to cavitation and oxidation. GBS diminishes and the intragranular deformation component dominates. or in other words. leading to rupture. ΔG is the activation energy. and 180MPa/1030oC (Kolbe et al. the creep behaviour of DS and SX alloys is therefore mainly a result of intragranular deformation. 1996). which are generally casted in the 001 crystal direction with the lowest modulus and hence the best tolerance to thermal fatigue. . 22 by adding the two components. 21. since most short-term creep tests conducted at high stresses would induce a large amount of intragranular deformation that over shadows the true failure mechanism at grain boundaries. (1). In summary. 1999) were used for calibration of the model to determine the parameter values of the model. There are other creep-curve equations. a DS alloy. (43). The model prediction is very close to the experimental observation. It should be recognized that the total (observed) secondary or minimum creep rate consists of both GBS and intragranular contributions with varying degrees. as shown in Fig. Now. (42) and (46). (43) is the θ-projection method proposed by Evans & Wilshire (1985) as ε = θ1 (1 − e −θ t ) + θ 3 ( eθ − 1) 2 4 (47) The θ-projection is purely empirical and mostly suitable for short-term creep tests where the secondary creep period is very short.. The creep data at 225MPa/950oC (Satyanarayana et al. the most similar one to Eq. Thus. Using the same approach.38×10-23 J⋅K-1) is the Boltzmann constant. Therefore. V is the activation volume. With the removal of grain boundaries. k (=1. σ0 is the back stress. which can be linked to intergranular and transgranular crack propagation. The model agrees well with the experimental creep behavior of CM247LC. the model can also be applied to SX alloys. at various stresses and temperatures are described with Eq. (43) provides a holistic description of creep for complex engineering alloys. For DS and SX alloys. let ε i = A0 exp ⎜ − ⎛ V (σ − σ 0 ) ⎞ ⎛ ΔG ⎞ ⎟ ⎟ sinh ⎜ kT ⎝ kT ⎠ ⎝ ⎠ (46) where A0 is the pre-exponential constant. 560MPa/840oC (DeMestral et al. creep life assessment based on the measured minimum creep rates may be erroneous by extrapolating short-term test data for long-term lifetime prediction. (43). The creep behaviors of CM247LC. advanced turbine blade and vane alloys are made from directionally-solidified (DS) and single crystal (SX) N-base superalloys. A schematic creep curve is shown in Fig. 2008). represents the total contribution from physical deformation mechanisms—GBS plus intragranular dislocation multiplication and climb.. ) 150 200 225MPa/950C-Exp.00E-01 5.-1) 4. 21.Life Prediction of Gas Turbine Materials 239 A0 (hr. 560MPa/840C-Exp. Activation Parameters for the CM247LC Creep Model 4.896×10-19 0 Table 4.00E+00 0 50 100 Time (hr.50E-01 1. 180MPa/1030C-EXp 225MPa/950C-Model 560MPa/840C-Model 180MPa/1030C-Model 186MPa/982C-Model Fig.22×1012 ΔG (J) V (m3) 2.063×10-28 σ0 (MPa) M 400 6. Schematics of creep curves representing GBS strain. intragranular strain and the total creep strain .50E-01 3.00E-01 3.00E-02 0. 22. Experimental and model creep curves of CM247LC.00E-01 Creep Strain 2. Fig.00E-01 1.50E-01 2. propagation of the dominant crack and its coalescence with internal creep cavitation damage. 1989. and 3) the strain-range partitioning (SRP) method (Halford et al. and inward propagation of the dominant crack. 1993). Recently. 1977). Subsurface cracks may also initiate at manufacturing flaws such as pores or inclusions. Oxidation also occurs first at the material surface or at existing crack surfaces or a crack tip. Sehitogulu. and more efficient analytical models for the dwell/creep-fatigue phenomena. A schematic of damage development in a material cross-section. leading to the final fracture. cavitation develops inside the material. more accurate. Creep/dwell ge dama Oxide scale σ Fig. Cracks may first initiate at surface flaws via intrusion/extrusion of PSB. Researchers have been trying to develop more descriptive. 2) the damage-rate model (Miller.1 The generic TMF model For generality. particularly along grain or interface boundaries. in order to understand the creep-fatigue interaction for component life prediction. coalescing with internal cavities or cracks along its path. multiple forms of damage may develop: an oxide scale forms at the material surface. creep cavities or wedge cracks may develop in the material interior. . The life evolution process in a metallic material at high temperatures can be envisaged as nucleation of surface cracks by fatigue and/or oxidation. 1992). 2009b). 23. which describes the processes of surface /subsurface crack nucleation. Evolution of material life under thermomechanical loading A gas turbine engine component generally experiences thermomechanical loading during start-up/shutdown (cyclic) and cruise (steady holds) which cause thermomechanical creepfatigue damage to the material.240 Gas Turbines 4. 23. a holistic model of dwell/creep-fatigue has been presented (Wu. as shown schematically in Fig. Under thermomechanical fatigue (TMF) loading. let us consider a polycrystalline material. but they will quickly break through the surface and become surface cracks. leading to final rupture. and fatigue damage may proceed in the form of persistent slip bands (PSB). 4. Oxidation damage penetrates the material inwardly through diffusion processes. Existing TMF models can be largely categorized into the following three groups: 1) the linear damage accumulation model (Neu & Sehitoglu.. In the mean time. the total crack growth rate is l +l da ⎛ = ⎜1 + c z dN ⎝ λ ⎞ ⎧⎛ da ⎞ ⎛ da ⎞ ⎫ ⎪ ⎪ ⎟ ⎨⎜ ⎟ +⎜ ⎟ ⎬ ⎠ ⎩⎝ dN ⎠ f ⎝ dN ⎠ env ⎭ ⎪ ⎪ (50) 4. (48). ΔN is the number of cycles during which the fatigue crack propagates between two cavities or between two ZSK cracks separated by an average distance of λ (λ~grain size or grain boundary precipitate spacing). particularly pronounced in high strength titanium alloys such as IMI 685. and it could cause significant low cycle fatigue (LCF) life reduction. Dwell fatigue of titanium alloys is often accompanied with faceted fracture along the basal planes of the α phase. i. the dominant crack only propagates by pure fatigue. as l + l ⎞⎛ da ⎞ da ⎛ = ⎜ 1 + c z ⎟⎜ λ ⎠ ⎝ dN ⎟ f dN ⎝ ⎠ (49) With environmental effects such as oxidation contributing to propagation of the dominant crack in a cycle-by-cycle manner. lz is the ZSK crack size. and Ti6242. bearing in mind that the functional dependencies of da/dN on the loading parameters are different for crack nucleation and crack growth.. as seen in Fig. Cavity growth has been recognized as a diffusion phenomenon. then we can rewrite Eq. we can use the term da/dN to represent both the rate of accumulation of irreversible slip offsets leading to crack nucleation as well as the fatigue crack growth rate. It has been perceived that the faceted fracture of α grains is driven by dislocation pile-up (Bache et al. Therefore. which act as nuclei for cracks. These two types of damage usually do not occur at the same time.. On the other hand.2 Cold-dwell fatigue Cold-dwell fatigue usually refers to fatigue with hold-times at ambient temperatures. also called Zener-Stroh-Koehler (ZSK) crack. 1997). . 24. da/dN~λ/ΔN. Here they are added together as competitive mechanisms over the entire temperature range from ambient temperature to near melting temperature.e. whereas wedge cracking is a result of dislocation pile-up. Wu & Au (2007) have treated the problem in terms of the kinetics of Zener-Stroh-Koehler crack formation. IMI 829 and IMI 834. These slip offsets may occur at the surface of grains or grain boundaries or interface boundaries.Life Prediction of Gas Turbine Materials 241 Fatigue damage can be regarded as accumulation of irreversible slip offsets on preferred slip systems. The coalescence of creep/dwell damage with a propagating fatigue crack will result in a total damage accumulation rate as expressed by lc + lz da ⎛ da ⎞ =⎜ ⎟ + ΔN dN ⎝ dN ⎠ f (48) where lc is the collective cavity size per grain boundary facet. creep damage may develop in the forms of cavities and/or wedge cracks (Baik & Raj. Assume that during the period of ΔN. Restricted slip reversal ahead of the crack tip is also recognized as the basic mechanism of transgranular fatigue crack propagation (Wu et al.. in a holistic sense. 1993). Note that usually creep cavitation occurs at a high temperature and ZSK cracks occur at a relatively low temperature. 1982). and n is the number of dislocations in a pile-up at time t. 25. which can be expressed as dn = ρ vs − κ n dt (51) where ρ is the dislocation density. According to the Orowan relationship. it should be recognized that the rate of dislocation pile-up accumulation is the net result of dislocation arriving by glide and leaving by climb in a unit time. s is the slip band width.242 Gas Turbines First of all. 24. Eq. A SEM micrograph of the fracture surface of IMI 834 failed by dwell faituge s κ v Fig. v is the dislocation glide velocity. Schematic of the kinetic process of dislocation pile-up. as n= γp κ [1 − exp( −κ t )] (53) Fig. κ is the rate of dislocation climb. γ p = ρbv (s ≈ b). (52). (51) can be rewritten as dn = γ p − κn dt (52) The number of dislocations in a pile-up at a steady-state can be obtained by integration of Eq. . Life Prediction of Gas Turbine Materials 243 Note that the energy release rate of a ZSK crack in an anisotropic material is given by (Wu. in the form of S-N curves. μ⎯shear modulus. we obtain lz = F22 b 2 ⎛ γ ⎞ 2 ⎡1 − exp( −κτ )⎤ ⎦ 16π ws ⎜ κ ⎟ ⎣ ⎝ ⎠ (57) For constant amplitude fatigue with a constant holding period. as shown in Figure 26 (b). (57) into (49) and neglecting cavity formation. (55). and microstructure (λ). this is the essence of “cold dwell” vs. F33 = μ. substituting Eq. indeed follows an exponential function. by the Griffith’s criteria: 2 F22 bT = 4 ws 8π a (55) where ws is the surface energy. the dislocation pile-up may create a mix-mode I-II crack. given the pure fatigue life as the baseline. and F22 = (F11 + F22 ) / 2 is the average modulus. when a dwell period is imposed on fatigue loading. we can find the crack size l (=2a) as l= F22 n2 b 2 16π ws 2 (56) Substituting Eq. . The model. (1997) studied IMI834 and plotted the dwell fatigue life as function of dwell time and stress as shown in Figure 26 (a) and (b). respectively. Eq. From Eq. Bache et al. and bT = nb is the total Burgers vector in the pile-up group. surface energy. describes the experimental behaviour very well. (53) into Eq. particularly in materials with fewer active slip systems at low temperatures. Basically. This means that. (58). (49) leads to N= Nf 2 ⎛ F b2 ⎛ γ ⎞ 2⎞ ⎜ 1 + 22 ⎜ κ ⎟ ⎡1 − exp( −κτ )⎤ ⎟ ⎣ ⎦ ⎟ ⎜ 16πλ ws ⎝ ⎠ ⎝ ⎠ (58) Equation (58) shows that the fatigue life is knocked down by a factor greater than one. in terms of the ratio of dwell-fatigue life to the pure fatigue life. 2005) G= ( ( bTi )Fij bTj ) 1 − K i Fij 1K j = 2 8π a (54) where Fij is an elastic matrix for anisotropic materials (F11 = F22 = μ/(1-ν). the dwelleffect will be more detrimental when the ratio of dislocation glide to climb is large. if damage occurs in the form of dislocation pile-up. (56). for isotropic materials). As temperature increases. Considering an average slip band angle of 45o. It shows that the dwell sensitivity. the integration of Eq. Hence. climb will overwhelm glide such that dislocation pile-up can hardly form. and most importantly it is controlled by the ratio of dislocation glide velocity to the climb rate in the material. but cavities may start to grow. This “knock down” factor depends on the material properties such as elastic constants. “hot creep”. dwell fatigue life can be predicted. and hence the dwell damage becomes minimal. .00E+04 Cycle s to Failure 1.00E+03 1.3 0.244 1 0.1 0 0 100 200 Dwell period (sec) 300 400 Gas Turbines Experimental Model (a) 1 cyclic 2min dwell exp 0.5min) 0. The simplest and hitherto the most popular way to count for the total accumulated damage is to combine Miner and Robinson’s rules (Miner.9 0.5 0.3 Creep-Fatigue Creep-fatigue interaction refers to the effect of cyclic-hold interactions at high temperatures where creep damage can be significant.7 0.6 0. 1945.9 model(2min) model (1.8 0.6 0. b) S-N curves with different dwell times.5min) model(1min) Peak Stress/UTS model(0.5 1.7 N d/N 0 0. as ∑Ni +∑t fi N tj rj =1 (59) . Robinson.00E+05 1.00E+06 (b) Fig. 26.2 0. (58) with the experimental data on IMI 834 (Bache et al.4 0. Comparison of Eq.00E+02 1. 4. 1997): a) normalized dwell fatigue life as a function of dwell time.8 0. 1952). is purely empirical and based on no physical mechanism. cc. and grain boundary sliding (GBS). Δεcc. (61) . we further assume that under cyclic-time hold conditions: 1. Δεpc. GBS contributes to intergranular fracture. pc and cp types of inelastic strains are contributed mainly from GBS during the transient creep. such that lc = ε gbs d where d is the grain size. such as persistent slip bands and fatigue cracking.Life Prediction of Gas Turbine Materials 245 where Nfi is the pure fatigue life at the ith cyclic stress or strain amplitude. The problem of this approach with respect to life prediction is that the actual partition of these strain components is difficult to determine within the total strain range imparted to the component by a random loading cycle. the hysteresis energy model (Ostergren. the accumulation of grain boundary damage. as cited by Viswanathan (1989). Considering physically that the total inelastic strain. strain relaxation (creep). 2. creep life fraction does not obey a linear relationship. leads to transgranular damage accumulation. When GBS operates. 3) plastic strain reversed by creep. 2) creep strain reversed by creep. and the strain range partitioning (SRP) approach (Halford et al. or in tension or compression whatsoever. and Nij is the number of cycles to failure if the entire inelastic strain is comprised of the named strain only. Δεpp. For short-period holds. Instead of modifying empirical equations with empirical factors accounting for the frequency effect. The intragranular deformation. Then. the SRP method tried to rationalize the complex creep-fatigue phenomena with the partition of four components in the total inelastic strain range: 1) plastic strain reversed by plasticity. Δεcp. the total failure life is expressed as Fpp Fpc Fcp F 1 = + cc + + N N pp N cc N pc N cp where N ij = Dij Δε ijij c (60a) (60b) Fij is the fraction of the named strain component. when proceeds in a cyclic manner. and 4) creep strain reversed by plasticity. as given by Eq. 1969). εg. since purely tertiary creep would never start upon short cycle repeats. (59). 27. and therefore. It does not differentiate the time spent under stress-control or strain-control conditions. 1977). εgbs. it is equivalent to the pp strain under cyclic conditions. either in the form of cavity nucleation and growth or as grain boundary cracks. A schematic of the occurrence of these strain components is shown in Fig. where Dij and cij are the Manson-Coffin constants. εin. which causes different material response as stress relaxation vs. is proportional to the GBS displacement. Many experimental investigations have shown that the fatigue life fraction vs. 1976). is comprised of intragranular deformation. as prescribed by Eq. and trj is the creep rupture life at the jth holding stress level. as straightforward as it may be.. The linear summation rule. Other creep-fatigue models were also proposed such as the frequency modified equation (Coffin. (1). Therefore. stress relaxation followed by reversed ramping to equal compressive strain. e) Tensile Hold Strain Cycle (THSC)—ramped to specific strain. again under constant amplitude cycling conditions. i. Eq. f) Compressive Hold Strain Cycle (CHSC)—opposite to THSC with compressive stress relaxation.e.. b) Compressive Cyclic Creep Rupture (CCCR)—ramped to a predetermined stress with compressive creep hold. lc can be stabilized once the entire hysteresis behavior is stabilized. reversed ramping to equal tensile strain. 27. c) Balanced Cyclic Creep Rupture (BCCR)—creep holds in tension and compression at constant load until specific strain reached. let lz = 0): N= ε gbs d 1+ λ Nf (62) . The SRP cycle profiles: a) High Rate Strain Cycle (HRSC)—constant ramping in tension and compression. (49) can be integrated to (in this case. neglecting dislocation pile-ups. d) Tensile Cyclic Creep Rupture (TCCR)— opposite cycle to CCCR with tensile hold. Under cyclic creep conditions as imposed by strain controlled cycles.246 Gas Turbines pp a) cc pc pp b) pp cp c) d) e) f) Fig. 306 0. environmental effects can be neglected. (1). Rene 80 at 871oC (C=0. as: Δε g = CN f −1/2 (63) which can be established by HRSC tests.289 0. THSC and CHSC.179 0.378 0. Test Type HSRC CCCR TCCR BCCR THSC CHSC Δεg pp pp+pc cp+cp pp pp+cp+cc pp+pc+cc Δεgbs 0 pc cp cc Δσ/E* Δσ/E* *Note that Δσ is the range of stress drop during stress relaxation in this test. TCCR.164 0. 29. as outlined in Table 5.605 0. For the bulk failure of these two materials under the test conditions.183 0.257 0. 1982) and re-establish the strain partitioning rule.385 0. Since GBS operates in shear. each individual grain is fatigued by the entire inelastic strain range. (62) to the asymmetrical creep-fatigue interaction tests such as CCCR.Life Prediction of Gas Turbine Materials 247 As discussed in section 3.208 0. d/λ=8) . The results are also shown in Fig. Table 5. Table 5 summarizes the strain partitioning of Δεg and Δεgbs for the different creep-fatigue interaction tests.254 0.111 Δεgbs 0 0 0 0 0 0.209 0.051 0. We take the data from a NASA contract report (Romannoski.283 0. ID 74-U-pp-13 21U-pp-8 41U-pp-10 22U-pp-9 42U-pp-11 92U-pc-13 28U-pc-9 91U-pc-12 98U-pc-16 29U-pc-10 112U-cp-11 86U-cp-9 30U-cp-5 31U-cp-6 36U-cp-7 Test HRSC HRSC HRSC HRSC HRSC CCCR CCCR CCCR CCCR CCCR TCCR TCCR TCCR TCCR TCCR Δεg 0. (25).1.308 0. respectively. Nf. 28 and Fig. is correlated to Δεg through Eq.554 0. according to Eq.322 0.026 0.08. it may produce grain boundary damage during either uniaxial tension or compression. the creep-fatigue interaction can be described by Eq. due to reversed plasticity. The Strain Partitioning Concept Spec.289 0.202 0.258 0. 145 642 1410 163533 217620 41 149 356 396 1415 101 147 193 530 3705 Table 6. For application of Eq.46 0. (62) for Rene 80 (in high vacuum) and IN100 (coated) as shown in Table 6 and 7.092 Nf 175 617 1997 94675 24606 209 448 969 961 1538 432 766 766 1479 5194 N 175 617 1997 94675 24606 45 137 363 390 665 125 222 253 565 2992 Exp. it should be recognized that. in comparison with the experimental data.204 0. the pure LCF life. but GBS contributes to the effect of additional intergranular fracture. 248 Spec. The advantage of this physics-based strain decomposition model is that.05 0 0. IN 100(Coated) at 900oC (C=0.196 0. ID 7 6 1 2 3 4 5 10 8 11 N12 N10 N9 39 N8 54 N5 56 Test HRSC HRSC HRSC HRSC HRSC HRSC HRSC HRSC HRSC HRSC CHSC CHSC CHSC THSC THSC BCCR BCCR BCCR Δεg Δεgbs Nf 0.026 0 0. once calibrated with coupon data.019375 0. 7.1 0. thus it provides a complete description for the mix mode fracture. Comparisons of Eq.085 0. it can be applied to component life prediction with εg and εgbs values evaluated from the constitutive model as presented in section 2. d/λ=50) 1 LCF M odel HRSC Creep-Fatigue M odel Inelastic Strain Range CCCR TCCR 0.129 0 0.16 0.01 10 100 1000 10000 100000 1000000 Cycles to Failure Fig.028 0 0.026875 0.031 0 0.09 0.054 0. .105 0. Mathematically. it unifies the SRP concept with the physical meaning that Δεg represents the intragranular damage and Δεgbs contributes to the intergranular fracture. (62-63) with experimental data for Rene 80 at 871oC It has been shown that Eq.0364.086 0 0.18 0.138 0 0.08 0. 28.168 0.059 0 0.11 N 796 905 696 1792 3806 5300 13788 19601 16901 67602 345 1202 1274 409 2070 1636 1834 4544 796 905 696 1792 3806 5300 13788 19601 16901 67602 128 601 647 174 1123 174 204 699 Exp.03375 0.121 0 0.016875 0. Gas Turbines 635 900 1260 2120 3670 9460 12210 17340 27260 48320 250 764 944 239 1495 159 200 383 Table. (62-63) can describe well the creep-fatigue interaction in complicated loading cycles.014 0 0.02 0.102 0. Al2O3. From the above relations. (62-63) with experimental data for IN 100 (coated) at 1000oC. f << 1. according to Eq. . and f is the volume fraction of the oxide scale. The stresses in both the substrate and oxide scale can be determined. Eox is the elastic modulus and αox is the thermal expansion coefficient of the oxide scale (~8μm/mK for Al2O3). i. the oxide.. σs is the stress in the substrate. e. 4. an oxide scale typically forms on the material surface. 29. by deformation compatibility: σ ox Eox and.4 Fatigue-Oxidation When gas turbine components operate in a hot gas environment.e. Comparisons of Eq. but usually has a higher modulus than the substrate.01 10 100 1000 Cycles to Failure 10000 100000 Fig. Therefore. may form with a negligible volume fraction. This layer of oxide will be forced to deform compatibly with the substrate until it breaks.1 0. by the force equilibrium + α ox (T − To ) = σs Es + α s (T − To ) (64) σ ox f + (1 − f )σ s = σ (65) where σox is the stress in the oxide scale.Life Prediction of Gas Turbine Materials 249 1 LCF M odel HRSC CHSC THSC Creep-Fatigue M odel Creep Fatigue M odel BCCR Inelastic Strain Range 0. Es is the elastic modulus and αs is the thermal expansion coefficient of the substrate material (~14μm/mK for Ni base superalloys). we can deduce that σ ox = Eox [σ + (1 − f )Es (α s − α ox )(T − T0 )] fEox + (1 − f )Es (66) In Ni-base superalloys.g.. which may lead to premature crack nucleation. To is the reference temperature at which the oxide formation is stress free. for creep-fatigue interaction. In hot creep. . acr. it provides a unified approach to deal with dwell/creep-fatigue interactions. (68) should become hc ⎤ dφ ⎡⎛ dφ ⎞ ⎥ = ⎢⎜ ⎟ + dN ⎢⎝ dN ⎠ f acr ⎥ ⎣ ⎦ (69) where acr is defined by acr = 1 ⎛ K IC ⎞ π ⎜ Yσ ⎟ ⎝ ⎠ 2 (70) KIC is the material fracture toughness. the pure mechanical fatigue component has been described by Eq. as long as the respective damage accumulation processes are described based on the relevant deformation mechanism. for simplicity. with the assistance of oxidation.e. 30. In cold dwell. leading to formation of ZSK cracks. The model has been shown to be successful in correlating both “cold” dwell-fatigue and “hot” creep-fatigue. Here. (50). as h = 2 kt (67) Neglecting other damage. Consider. lc =lz = 0. Some OP and DP TMF data are also shown in Fig. If we normalize the crack length with the critical crack length.5 Summary A nonlinear creep/dwell-fatigue-oxidation interaction model is derived based on nucleation and propagation of a surface fatigue crack. the oxidation stress may change with temperature. Suppose the oxide growth follows a parabolic relation. i. Therefore.1. the damage is envisaged as dislocation pile-up. (69) and the diffusion constant given by Neu & Sehitoglu (1989). 4. these data fall closer to the line representing the oxidation-fatigue interaction. (25) in section 3.250 Gas Turbines (66). the shape factor Y is assumed to be unity and the fracture toughness is 60 MPa√m. Eq. the damage accumulation is related to grain boundary sliding. Particularly. During a TMF cycle. the model reconciles the SRP concept. the fatigue-oxidation interaction results in the crack growth rate as: ⎤ da ⎡⎛ da ⎞ = ⎢⎜ ⎟ + hc ⎥ dN ⎢⎝ dN ⎠ f ⎥ ⎣ ⎦ (68) where hc is the critical penetration length. and its coalescence with creep/dwell damages (cavities or wedge cracks) along its path inside the material. the life prediction for IN738 LCF at 900oC LCF is shown in Fig. then. 30.. the high temperature effect on LCF and TMF life of IN738 can largely be attributed to oxidation. from Eq. The prediction agrees well with the experimental data. for example. With oxidation kinetics as described by Eq. Y is the crack configuration factor. oxides act as stress raisers at the surface (multiplied by Eox/Es). As the comparison shows. IN738. 30.03’) acknowledging the minimum detection limit of non-destructive inspection (NDI). pure fatigue in IN738 at high temperatures. which is very important for ensuring structural integrity of critical gas turbine components such as discs. Macroscopic crack growth is usually the last stage of damage accumulation leading to catastrophic fracture of components. The microstructural damage processes that contribute to crack growth always involve certain deformation mechanisms with the influence of environmental effects. keeping consistent with that discussed in the previous sections. a < 0.1 10 100 1000 number of cycles to failure 10000 100000 Fig. .g. When the damage state presents itself as a macroscopic crack. Macroscopic crack growth and damage tolerance The previous section deals with the material life evolution under a nominal stress when the material damage state does not alter the stress distribution in a component macroscopically. this section will also treat the subject with considerations of the fundamental crack growth mechanisms and deformation kinetics. This is usually called the crack initiation life with an engineering definition (e.002 Hz) 10 LCF. 400 C pure f atigue model f or 900 C pure f atigue model f or 400 C strain range (%) f atigue+oxidation model f or 900 C 1 0. Understanding the crack growth process is a priori for accurate prediction of crack growth life. using physics based crack growth models for accurate life prediction. Therefore. then fracture mechanics concepts have to be used to characterize the stress-field ahead of the crack tip and the subsequent crack growth processes.Life Prediction of Gas Turbine Materials 251 IN738LC (f=0. 900 C OP 400-900 C DP. 5. While focusing simplified methodologies for engineering application. one needs to relate the observed behavior to the controlling physical mechanism. 400-900 C LCF. to break through the curtain of phenomenological description. Fatigue-oxidation interaction vs. Depending on the material and the applied condition. 5. 2005). . Then. 31. as briefly introduced in the following. In general. and III) the out-of-plane shearing mode. it is meant to be applied to fracture of materials under the so-called small-scale yielding condition. i. may proceed in three distinguished modes: I) the opening mode. In most practical cases. II) the in-plane shearing mode.e. 31. The solution is obtained by solving the stress equilibrium and strain compatibility equations with given boundary conditions and the appropriate constitutive equations (such as Hooke’s law for elasticity or some power-law for plasticity). however. as schematically shown in Fig. that is.252 Gas Turbines 5. A schematic of crack opening modes. and ii) non-linear fracture mechanics.1 Fundamentals of fracture mechanics Fracture mechanics is the theory to describe the stress problems of cracks in continuum solids. based on the theory of elasticity. perpendicular to the maximum principal stress. Fig.1 Linear-Elastic Fracture Mechanics Linear-elastic fracture mechanics (LEFM) has been developed for crack problems in elastic continua. fracture. the crack length is much longer than the plastic zone developed ahead of the crack tip.. opening of the crack. fracture mechanics are categorized into i) linear elastic fracture mechanics. crack growth mostly proceeds macroscopically in mode I. Details of LEFM may be seen in the book—Fracture Mechanics: Fundamentals and Applications (Anderson. For engineering practices. the parameter derived from the crack-tip stress field or energy is used to characterize the fracture processes in engineering materials.1. Rice. and fij(θ) is an angular function. K-solutions for various standard configurations have been summarized in handbooks (e. An alternative method to extract stress intensity factors is the weight function method (Bueckner. this method can be used to evaluate the stress intensity factor by integrating the stress distribution with a weight function over the crack plane for an elastic body under an arbitrary loading. 32. Newman & Raju (1983) have also provided numerical solutions for elliptical cracks in some standard 3D bodies.46 ⎜ ⎟ ⎝c⎠ 1. 1970. where r is the distance from the crack-tip and θ is the position angle) can be expressed as σ ij = KI f ij (θ ) 2π r (71) where KI is the (mode-I) stress intensity factor. But. which can be quite tedious and time consuming. the mode-I stress field ahead of the crack-tip (in the coordinate systems as shown in Fig. y r θ x Fig. as: crack . 1972). meshing for the particular component-crack geometry. the stress intensity factor is given by K I = Yσ π a (71) where σ is the nominal applied stress and Y is the component geometry factor. 2000). the stress intensity factor is given by K I = Yσ πa Q (72a) where ⎛a⎞ Q = 1 + 1.65 (72b) which is an approximation of the elliptical integral of the second kind to the 2nd power. Based on the reciprocal theorem of elasticity. The crack-tip coordinate.Life Prediction of Gas Turbine Materials 253 In a two dimensional (2D) crack configuration. For a crack of elliptical shape with a short axis 2a and long axis 2c. 32. Tada et al. in most cases for cracks in engineering components. the solution is sought numerically using finite element methods.g. For a 2D crack of length 2a. but the question is how to determine the weight function for the body? T σ(x) a σ(x) = a Fig. P′)dAP (73) where P is the integration point. 4) are the distances between point C. 34. the weight function method can be generally expressed as (Bueckner. Schematic illustration of the weight function method: a) stress distribution induced in the uncracked body subjected to an arbitrary remote traction T. and m(P. 33. For two dimensional (2D) cracks. P′) is the weight function. since the stress distribution σ(x) on the presumed crack plane can be readily determined using the finite element method for an engineering component.a) is the weight function for the body. σ(x) is the stress distribution as induced by the remote traction T in the uncracked body. and the four points on the crack front that connects to point C with lines intersecting perpendicularly to crack front. as illustrated in Fig. P′) = 2s 1− s s s s − − − 8 ρ1 8 ρ 2 8 ρ 3 8 ρ 4 (74) π 3/2 l 2 where s is the shortest distance from P to the crack front. and m(x. y ))m( P . This method is rather attractive for engineering applications. 1978.254 Gas Turbines K = ∫ σ ( x )m( x . 33. P’ is the crack-front point where the stress intensity factor is to be evaluated. where the extension of the shortest distance line intersects the major axis of ellipse. as shown in Fig. 1985) K P′ = ∫∫ σ ( P( x . and b) the same stress distribution loaded on the crack surface. ρi (i =1. a)dx 0 a (73) where. . An example for an embedded elliptical crack in an infinite solid was given by Wang et al. y . (1998): m( x . 2. Rice. 3. the crack-tip stress field can be described by ⎛ ⎞ J σ ij = σ 0 ⎜ ⎜σ ε I r ⎟ ⎟ ⎝ 0 0 n ⎠ 1/( n + 1) σ ij (θ . 1976): ∂u ⎞ ⎛ C (t ) = ∫ ⎜ Wdy − T ⋅ ds Γ ∂x ⎟ ⎝ ⎠ (77) .g. in this case. the J-integral. monotonic plasticity. and s is the arc length along the contour Γ. the stress field can be found to be controlled by another time-dependent path-integral (Landes & Begley. Weight function for an elliptical crack. e. the crack-tip parameter for nonlinear materials is defined by contour-independent energy integrals. For materials exhibiting time dependent deformation.Life Prediction of Gas Turbine Materials 255 P s ρ1 C ρ2 P l ρ3 Fig. Then.. which is defined by ∂u ⎞ ⎛ J = ∫ ⎜ Wdy − T ⋅ ds Γ ∂x ⎟ ⎝ ⎠ (76) where u is the displacement vector.2 Non-linear fracture mechanics Nonlinear fracture mechanics generally deals with crack problems in materials with nonlinear constitutive behaviours. since it is not universally valid for all materials. after Hutchinson (1968) and Rice & Rosengren (1968). the way to extract the stress intensity as in the linear elastic material is not desirable from the mechanics point of view. ρ4 5. similarly. Therefore. W is the strain energy density. 34. Hence. The singularity of the crack-tip stress field in a nonlinear material depends on the material’s strain hardening exponent.1. T is the surface traction vector. n) (75) which is known as the HRR field. 1974. respectively. Fatigue crack growth mostly proceeds in a transgranular mode. Δ K th = kT ⎥ Vf Vr ⎟ α f V r . as kT/VH << 1. τ0f = τ0r and γ 0 f = γ 0 r . and the subscripts “f” and “r” refer slip-forward and reversal. following a power-law relationship with the cycle stress intensity factor range.α rV f ) da ⎟ . particularly because of the structural integrity airworthiness requirements. which has been summarized as the restricted slip reversibility (RSR) concept. H is the work-hardening coefficient. 1988).R)V f V rH ⎝ ⎠ 2 (80) where kT ⎤ ⎡ ⎛ V f H γ of ⎞ V f H ⎥ ⎢ ⎜ ⎟ ⎢ ⎥ ⎜ 2f α f ΔK ⎟ ≠ (1 . Vf = Vr = V. = ( ΔK . α is the fracture work factor. f is the frequency. as schematically show in (Fong & Thomas.2 Fatigue crack growth Fatigue crack growth phenomena have been an important subject of study. and both forward and reverse slips occur by the same mechanism so that ΔG≠f = ΔG≠r. The fatigue crack growth law or model is a cornerstone of the so-called damage tolerance design. for pure mechanical fatigue: .α rV f ⎢ H ⎜ ⎠ ⎢ ⎝ V rH ⎥ ⎛ V rH γ or ⎞ ⎢ ⎥ ⎜ ⎜ 2f α ΔK ⎟ ⎟ r ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ (81) where γ 0 is a pre-exponential strain rate constant.R)HV f V r ⎢ 1 ⎛ ΔG ≠ ΔG r ⎞ f ⎥ ⎠ ⎜τ of .256 Gas Turbines In elastic materials or under small-scale yielding conditions. Based on the RSR concept and the deformation kinetics. k is the Boltzmann constant. It has been recognized that the alternating slip and slip reversal process is mostly responsible for fatigue crack nucleation and propagation (Neumann.ΔK th )⎜ ⎜ σy ⎟ dN 12π (1 . This section concentrates on fatigue crack growth mechanism and its rate equation. ΔK. 1963): da = C( ΔK )3 . where the microstructure (grain size. V is the activation volume. the J-integral and the stress intensity factor can be related as: J= K2 E (78) 5. 1982). Wu et al. αf and αr are of the same order of magnitude. T is the absolute temperature.ln ⎝ . In mechanical fatigue.τ or + ⎟ . Therefore. which will be elaborated later. and hence ΔKth approaches zero. ΔG≠ is the activation energy. τo is the slip resistance of the lattice. (1993) have derived a transgranular fatigue crack growth rate equation as ⎛ ΔK ⎞ (α f V r . Laird & Smith. precipitate size and shape) is stable and environmental effects are absent. dN (79) where C and n are empirical constants. as first observed by Paris (Paris. 35. 1988) and n = 2. For example. the values predicted by other models.Life Prediction of Gas Turbine Materials 257 (a) (b) Fig. This process may be repeated over several load cycles (N) to produce a final crack length increment. (iii) During the decreasing load cycle. as shown in Fig. the RSR model shows that the fatigue crack growth rate depends on the materials’ yield strength inversely to a power of 2. slip systems on two favourably oriented slip planes S1 and S2 are activated. 1989). 1973). In addition.92 in offshore steels (Smith & Cooper. (ii) Forward slip occurs solely on S1 during the rising load cycle. after which a similar process may occur on another favourably oriented slip system variant along another pair of parallel slip planes. producing a slip step of length lf. an increment of slip reversal lr occurs on S1. This was indeed observed for fatigue crack growth rate data of a variety of alloys tested at room temperature in vacuum (Speidel.7~3. (α f . The dependence of fatigue crack growth rate on yield strength was . Numerous experiments have also shown that the power law exponent of the Paris law falls within the range of 2. as shown in the schematics (v) to (viii).. (b) The RSR is confined within the plastic zone. ΔK relationship in a log-log plot exhibit a slope of 3 in the Paris regime. (iv) A final slip reversal occurs on S2. S3 and S4. This implies the dependence on microstructure and temperature. the yield strength depends on the grain size through the HallPetch relationship and it is also a function of temperature. 36. and it is also inversely proportional to the work-hardening coefficient.α r ) da = ( ΔK )3.4 within the Paris regime. Interestingly also. Therefore. (a) Schematics of fatigue crack growth by RSR: (i) Upon loading. where crack growth rate vs. The power law exponent values found in these experiments are closer to 3 than 2 or 4. it may be fairly concluded that the RSR model is suitable for conventional materials where deformation is promoted by homogeneous slips. Pure fatigue is essentially a “low temperature” phenomena occurring by the mechanism of dislocation glide. dN 12π (1 . lf –lr.R)VHσ 2 y (82) Equation (82) takes the form of the Paris relationship with a physically defined proportional factor and a power law exponent of 3. it was reported that n = 3 represents fatigue crack growth in ductile steels (Miline et al. producing a sharp crack tip. as depicted by the RSR model. H-compensated fatigue crack growth rate vs. 36.5Mo-0. which is far above the fatigue threshold of this material. A range of yield strength values. The work hardening coefficient. for each heat-treated material is estimated by dividing the difference between the ultimate tensile strength and the yield strength with the elongation. varying between 466 MPa and 834 MPa. σy2 for 0. Fig.5Cr-0.69 MPa√m. are plotted against σy2 as shown in Fig.258 Gas Turbines demonstrated by Benson and Edmonds (1978) on 0.5Cr-0. 37. the H-compensated crack growth rates at ΔK = 15.25V steel. were obtained using different heat treatment procedures. Fatigue crack growth behaviours of a number of metals at room temperature in vacuum. . H. Then. 37. typically 13%.25V steel. Fig.5Mo-0. Vitek. & de los Rios. 1978. Xu et al.3 Tm. as schematically shown in Fig.3 Creep crack growth Creep crack growth resistance is also one of the important damage-tolerance properties required for materials being used for high temperature applications (T ≥ 0. leading to reduction of the activation barrier ΔG≠r. due to crack closure. corrosion fatigue is a complex process and the detailed kinetics of the involved chemical processes need to be considered. and therefore it is still lacking of a universal treatment to both creep-ductile and creep-brittle cases. Indeed.Life Prediction of Gas Turbine Materials 259 Equations (80)-(81) further predicts that the threshold in fatigue crack growth does not occur in the absence of microstructural change and environmental effects ahead of the crack tip such as in the case of pure mechanical fatigue.g. the complexity of the behaviour and the scatter reflects the interaction of the crack propagation kinetics with the microstructure. which indeed supports the predication of Eq. (81). 1986. While the underlying physical mechanism is the same as discussed above. which should be addressed with a probabilistic approach and it is beyond the scope of this chapter. and/or increase of Vr upon slip reversal. 1977). Riedel. an intrinsic fatigue threshold may arise as a result of environmental interactions in a way if the environmental effects weaken the point obstacles after a new crack surface is exposed. Dimelfi & Nix. According to Eq. which were good for creep-ductile materials such as Discaloy (Landes and Begley. Many mechanism based creep crack growth models have been proposed (e. J. 1990). Because of its apparent time-dependence. Some apparent thresholds ΔKth does occur in coupon testing using load-decreasing procedures. 1976) and steels (Liu and Hsu. where Tm is the absolute melting temperature). which is really a mixed creep-oxidation condition. Riedel. for high strength heat resistant alloys such as superalloys (Floreen. however. since load shedding conditions are not particularly relevant to the service condition for fatigue crack growth to occur. 1977. 1982) and some general fracture mechanics treatments have also been given (Saxena. which will not be discussed further. On the other hand. 38. the stress intensity factor (K) has also been used to correlate CCGR. and τ0r. especially under small-scale creep deformation conditions and in the presence of environmental embrittlement effects. Another important phenomenon of fatigue is the behaviour of short cracks (Miller. (82). 1989. Cocks & Ashby. 1985). It is noteworthy though. that small crack growth behaviour is often observed to occur below the fatigue threshold established for a long crack. 1986). Sadananda & Shahinian. early studies on creep crack growth (CCG) mainly focused on correlating creep crack growth rates (CCGR) with some pathindependent energy integrals C(t) and C* (the steady-state value of C(t)). Most creep crack growth tests have been conducted under constant load at high temperature in air. K. Considering the crack-tip stress relaxation by two deformation mechanisms—intragranular deformation and GBS. (1999) has derived a creep crack growth equation in the following form: ⎡ da d ⎢ n + 1 ⎛ AI n ⎜ = ⎢ ⎜ dt λ ⎢ n − p + 1 ⎝ BI p ⎢ ⎣ ⎞ n−1 ⎛ 1 ⎞ p − 1 p − 1 p − 1 ⎛ C (t ) ⎞ ⎟ C (t ) + ( p + 1) ⎜ B KI ⎜ ⎟ ⎟ ⎜ ⎟ ⎟ ⎝ 2π ⎠ ⎝ In ⎠ ⎠ 1 2p 1 2 p2 − p − 2 p2 −1 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ (83) . 5. 1983. but these models did not sufficiently considered the contribution of grain boundary sliding. as discussed in section 2&3.2 Creep-brittle cases In creep brittle materials (e. crack-tip deformation will mostly be concentrated in the grain boundary region.260 Gas Turbines where n and p are power-law index. 38. 5. the creep zone may contain many grains. (83) dominates such that da d n + 1 ⎛ AI n ⎜ = dt λ n − p + 1 ⎜ BI p ⎝ ⎞ n−1 ⎟ C (t ) ⎟ ⎠ 1 (84) This model basically agrees with that of Cocks & Ashby (1982). In and Ip are HHR field parameters associated with the HRR field of intragranular deformation and GBS.g. while the contribution of GBS may be relatively small.. 5. considering that for pure GBS. the second term of Eq. (83) dominates. A schematic of stress distribution in three zones ahead of a creep crack tip. as given by . the rate equation reduces to: da 3 d = BK 2 dt 4π 2 λ (85a) The proportional constant B depends on grain boundary diffusion and microstructure. the first term in Eq. Fig. and therefore intragranular deformation plays a significant role in stress relaxation. d is the grain size and λ is the critical GBS distance between cavities. For these cases. and therefore GBS plays a dominant role in the crack growth process. respectively.3. p = 2. and particularly. cast Ni-base superalloys) containing large grains. In such cases.3. A and B are power-law constants. In that case. the role of intragranular deformation in crack-tip stress relaxation and creep crack growth will be limited.1 Creep-ductile cases In creep ductile materials with small grain size. Life Prediction of Gas Turbine Materials 261 B= Dgb μ b ⎛ b ⎞q ⎛ λ + h ⎞q − 1 ∝ d −q kT ⎜ d ⎟ ⎜ b ⎟ ⎝ ⎠ ⎝ ⎠ (85b) Creep crack growth behaviours on Udimet 520 at 540oC can be taken as an example to illustrate the application of Eq. (85) (Xu et al., 1999). The material was heat treated to obtain different grain sizes, all containing intragranular γ′ but without any grain boundary M23C6 precipitates, and tested in argon and air. The test temperature was selected to ensure that no grain boundary precipitates formed during testing. Fractographic studies revealed that predominantly intergranular fracture and extensive crack tip branching occurred both in air and in argon, as shown in Fig. 39 (a) and (b) respectively. The metallurgical evidence suggests that GBS-controlled intergranular cracking and oxidation were the dominant damage mechanisms. No evidence of cavitation was found in any of the specimens. The test and material conditions satisfy the model’s assumptions of the dominance of GBS. (a) (b) Fig. 39. SEM micrographs of the creep fracture surface of Udimet 520, (a) in air and (b) in argon, after Xu et al. (1999). The CCGR in the argon environment, plotted in a double logarithm scale against the stress intensity factor K, exhibits a linear behaviour with the slope of 2, as shown in Fig. 40. For Udimet 520 with planar grain boundaries and no grain boundary precipitates, the stress index of GBS rate is 2 and hence, as predicted by Eq. (85), the creep crack growth rate exhibits a dependence on the stress intensity factor (K) to a power of 2. Other existing models fail to predict the K2 dependence for creep crack growth in an inert or vacuum environment. With regards to microstructure-dependence, the present creep crack growth model predicts that the creep crack growth rate depends inversely on the grain-size dependence to a power of q which can be related to grain boundary precipitate distribution morphology. For materials with planar and clean grain boundaries (no grain boundary precipitates, q = 1), it predicts no grain-size dependency. The data on Udimet 520 showed that the CCGR data were not sensitive to grain size variation over a grain size range of 235-464 μm, which corroborated the model prediction. For superalloys having received standard heattreatments, where discrete grain boundary precipitates (e.g. M23C6 or δ phase) are present, the model predicts an inverse grain size dependence of creep crack growth rate. As reported in the literature, coarse grain size superalloys usually exhibit lower creep crack growth rates 262 Gas Turbines (Floreen, 1983). For example, an inverse relation between CCGRs and grain size has been reported for Alloy 718 at 650°C (Liu et al. 1991). Stronger grain-size dependence is predicted by the model for materials with a continuous grain boundary precipitate network that may result from overaging or extended service exposure. However, no experimental work has been reported in this regard. But, it is a serious issue concerning aging gas turbine components. Fig. 40. Creep crack growth rate in Udimet 520 in argon and air at 540oC. Considering environmental effect, as shown in Fig. 40, the creep crack growth rate in Udimet 520 tested in air exhibited an increasing power-dependence on K from 2 to a high value of 6.5 as K increases. This change in the K-dependence of creep crack growth rate with the environment, i.e. argon versus air, suggests that oxidation has a strong influence on the creep crack growth process. The oxidation effects can be attributed to the reduction of the critical GBS distance λ to advance the crack in Eq. (85). An effective λ in the presence of oxide penetration may be equal to λ0-X, where λ0 is the critical GBS distance in the absence of oxidation effects, and X is the penetrating oxide depth measured from the external oxide surface. As time t increases, oxides will penetrate deeper into the material and λ will be significantly reduced, and therefore the creep crack growth rate will increase. Taking the effect of oxidation into consideration, Eq. (85) takes the form da 3 d BK 2 = dt 4π 2 λ0 − X (86) The curve for the creep crack growth rate in air was fitted to the test data by Xu et al. (1999) using a semi-empirical approach (Xu et al. 1999). Life Prediction of Gas Turbine Materials 263 5.4 Creep-fatigue interaction in crack growth Crack growth under creep-fatigue conditions is another important phenomenon affecting the structural integrity of gas turbine components, since evidently most of them operate under such conditions during the takeoff-cruise-landing cycle of the aircraft. The subject has been treated by Saxena et al. (1981) who proposed a linear summation model as: 2 2 ⎤ th ⎡ K (1 − ν ) da ⎛ da ⎞ * =⎜ ⎟ + C 5 ∫0 ⎢ E(n + 1)t + C ⎥ dt dN ⎝ dN ⎠ f ⎢ ⎥ ⎣ ⎦ m (87) where th is the hold time; n is the creep law exponent, and m ~ 1 or n/(n+1) (Cocks & Ashby, 1982), and C5 is an empirical constant. Eq. (87) naturally reduces to a creep crack growth equation for long-term hold-times, and though it resolves into a K-dependence for short-term hold times but relates to no strong microstructural dependence, which is contrary to most experimental observations (e.g., Bain et al., 1988; Telesman et al. 2008). Recall that, in section 4.1, we have developed a generic thermomechanical fatigue model with consideration of oxidation-creep-fatigue interactions, Eq. (50). Now, it is reasonable to consider that under creep-fatigue conditions, grain boundary sliding operates at a stress close to σy within the plastic zone, which is responsible for producing intergranular damage proportion to lc = d ∫ ε gbs dt 0 th (88) Referring to Eq. (8) but omitting the mathematical detail of the integration, we shall propose for simplicity that p lc ∝ d 1 − qσ y th (88) Hence, substituting Eq. (88) into (50), we obtain: da p = 1 + Bλ −1d 1− qσ y th dN ( da ⎨⎜ ) ⎪⎛ dN ⎞ ⎟ ⎠ ⎪⎝ ⎩ ⎧ f ⎛ da ⎞ ⎫ ⎪ +⎜ ⎬ dN ⎟ env ⎪ ⎝ ⎠ ⎭ (89) The creep-fatigue crack growth rates in Udimet 720 observed by Bain at al (1988) are shown in Fig. 41. It shows strong grain size dependence in the crack growth behaviour. Taking the fatigue crack growth rate at 427oC as the reference for each grain-size material respectively, this grain size dependence of creep-fatigue crack growth rate in Udimet 720 can be described using Eq. (89) with q = 2.5688, as shown in Fig. 42. Note that the yield strength of these materials were almost the same and there were grain boundary phases such as TiC, Cr23C6, and (Cr, Mo, W)3B2 present to form a discrete/almost continuous distribution such at 2 < q < 3. The pure fatigue crack growth components (neglecting oxidation) in these materials were: da = 6.432 × 10 −11 ΔK 3.72 ( ASTM 0) dN da = 1.6 × 10 −11 ΔK 3.72 ( ASTM 3 − 8.5) dN (90) 264 Gas Turbines Fig. 41. Fatigue crack growth at 649oC with 5 min hold time at the maximum load (Bain et al., 1988). Fig. 42. The predicted Fatigue crack growth in Udmet 720 at 649oC with 5 min hold time. Telesman et al. (2008) also observed strong microstructural dependence of the hold time fatigue crack growth rate in the LSHR P/M disk superalloy. Using heat treatments to control the grain size at constant but with different cooling rate and subsequent aging treatments to control the γ’ size, they related the increased fatigue crack growth rate with the stress relaxation potential possessed in each microstructure with different (primary, secondary and tertiary) γ’ sizes and distribution. This can also be explained qualitatively by Life Prediction of Gas Turbine Materials 265 Eq. (89): stress relaxation would impart a lower grain boundary sliding rate, resulting in lesser grain boundary damage during the hold time and hence reducing the overall crack growth rate. Finally, it should be pointed out that none of the above phenomena could be sufficiently addressed with Eq. (87). In general, the present model, Eq. (89), also presents the effect of creep damage in a multiplication factor, for every fatigue crack increment will induce coalescence with the creep damage accumulated ahead of the propagating fatigue crack. 5.4 Damage tolerance analysis The damage-tolerance philosophy assumes materials or components entering into service have defects in their initial conditions. Then the component life is basically the life of crack propagation starting from an initial flaw, as: N=∫ af da f ( ΔK ) a0 (91) where a0 is the initial crack size, af is the final crack size at fracture (or sometimes, a dysfunction crack size reduced by a safety factor), and the crack growth rate function f(ΔK) can be any of the aforementioned, particularly Eq. (79), (86) or (89), depending on the operating condition. In the simple case under pure mechanical fatigue condition, where the crack growth rate is expressed by the Paris law, Eq. (79), the damage tolerance life can be obtained by integration as da C ( ΔK ) n N=∫ af a0 =∫ af da C Δσ π a0 ( ) n n a2 ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ n − n ⎟ = n n ( − 1)C Δσ π ⎜ a 2 − 1 a 2 − 1 ⎟ ⎜ 0 ⎟ f 2 ⎝ ⎠ ( 1 ) (92) Using this philosophy, components need to be inspected before and during service. If no actual cracks are found, it is usually assumed that the initial crack size is equal to the nondestructive inspection (NDI) limit, and hence the crack propagation life marks the safe inspection interval (SII) on the maintenance schedule. Since crack propagation life is apparently sensitive to the initial crack size, an economical maintenance plan requires more advanced NDI techniques with accuracy and lower detection limits. Taking advantage of the damage tolerance properties, a component can repeatedly enter into service, as long as it passes NDI, regardless of whether the usage has exceeded the safe-life limit, and it will retire only after cracks are found. This is called retire for cause (ROC). By virtue of damage tolerance, life extension can be achieved on safe-life expired parts, as shown schematically in Figure 5.1. The damage tolerance approach is not only meant to be used as a basis for life extension, but more so to ensure the structural integrity of safety-critical structures and components to prevent catastrophic fracture, as it is required by the Aircraft Structural Integrity Program (ASIP) and Engine Structural Integrity Program (ENSIP) of the United State Air Force. Due to the inherent properties of materials, detectable crack propagation periods are usually very short for most materials, and even more so for advanced materials such as intermetallic and ceramic materials, such that life management based on damage tolerance is totally unpractical (too many interruptions of service due to inspections, and therefore too costly). Besides, it is commonly recognized that damage accumulation spends most of its time 266 Gas Turbines undetectable non-destructively, i.e., at the microstructural level and in the small (short) crack regime. Thus, new life management philosophy is required, which should put emphasis on the physics-based understanding of the continuous evolution of damage from crack nucleation, to short crack growth and long crack growth (to eventual failure), which will be called the holistic structural integrity process. n inspections if no crack are found Dysfunction size …… NDI limit Fig. 43. Schematic of damage–tolerance life management. Life 6. Analyses of gas turbine components This section demonstrates the application of the aforementioned models for two selected cases: (i) turbine blade creep and (ii) turbine blade crack growth, as follows. 6.1 Turbine blade creep A turbine blade is modelled using the finite element method, as shown in Fig. 44. The blade was represented by a solid airfoil attached to a solid platform. Since the present analysis focused on the airfoil portion, the platform only serves as the elastic boundary condition. The temperature and pressure distribution induced by the hot gas impingement is obtained from fluid dynamics and heat transfer analyses and is applied upon the blade as the boundary conditions as shown in Fig. 45 and Fig. 46, respectively. The turbine rotates at 13800 rpm. The turbine blade material is assumed to creep by GBS only, obeying the following creep law: ε gbs = ε 0 + φ ε sst + σ β H gbs 2 ⎡ ⎛ β 2φ H gbs ε sst ⎞ ⎤ ⎢1 - exp ⎜ ⎟⎥ ⎜ σ ( β - 1) ⎟ ⎥ ⎢ ⎝ ⎠⎦ ⎣ (93) where E = 100000 (MPa), Hgbs=25000 (MPa), β = 1.00925, and ε ss = 108 exp ⎜ −4 − ⎝ ⎛ 16000 ⎞⎛ σ − 150 ⎞ T ⎟⎜ E ⎟ ⎠⎝ ⎠ 2 (94) Life Prediction of Gas Turbine Materials 267 9370 9468 9552 9636 1 302 560 818 1119 9734 Fig. 44. FEM model of turbine blade. The numbers indicate some selected nodes. Numbers indicate the nodal points Fig. 45. Temperature profile in the blade In both cases. The stress relaxation or “stress shakedown” in a component have a two-fold meaning on the life of the component: it may impact on the low cycle fatigue damage with a timely reduced stress. After 50 hours. but on the other hand. Stress concentration remained at the bottom attachment.Marc for 100 hours. Pressure profile as the boundary condition on the blade surface. 50 Fig. which then leads to stress relaxation. After 100 hours. especially the upper half. practically remains in the elastic regime. 48. respectively.268 Gas Turbines Fig. Except those creep strain concentration regions. Creep deformation and stress relaxation curves at selected nodes along the leading/trailing edges (the nodal numbers are indicated in Fig. the majority of the airfoil. when creep deformation proceeds into a steady state. which results in a highly nonuniform stress distribution in the blade with particular stress concentrations at the midleading edge and mid-trailing edge and near the bottom attachment. 46. stress distribution became more uniform throughout the airfoil. respectively. for simplicity of demonstration. The initial (at t = 0) and final (t=100 hours) von Mises stress distribution contours are shown in Fig. Creep simulation was conducted using MSC. the stress has dropped dramatically with the overall increment of the creep strain. The creep strain accumulates the most where the initial elastic stress concentration appears. From this analysis for this particular blade. the platform was assumed to deform only elastically. 47 and Fig. . The final creep strain distribution contours are shown in Fig. because. 53. it is also accompanied with an increase of creep damage in the material. 49. The initial response of the blade is purely elastic. creep deformation proceeds in steady state. 44) are shown in Fig. it deems that the mid-leading edge and the bottom of trailing edge are critical locations. . and b) the suction side. 47. Stress distribution at t=0: a) the pressure side.Life Prediction of Gas Turbine Materials 269 (a) (b) Fig. 48. a) the pressure side. and b) the suction side. . Stress distribution at t =100 hrs.270 Gas Turbines (a) (b) Fig. . a) the pressure side. and b) the suction side.. 49. Creep deformation of the blade after a 100 hr.Life Prediction of Gas Turbine Materials 271 (a) (b) Fig. Deformation history at selected nodes along the leading edge. . Stress relaxation at selected nodes along the leading edge. 50. 51. Fig.272 Gas Turbines Fig. Fig.Life Prediction of Gas Turbine Materials 273 Fig. Deformation history at selected nodes along the trailing edge. . 53. Stress relaxation at selected nodes along the trailing edge. 52. which drove the crack toward a “circular” shape. Simulation of crack growth was conducted using the weight function method. The results of the weight function method crack growth simulation are seen to agree with the observed crack growth profile on an actual component. The von Mises stress in a turbine blade. then the stress intensity factor at the surface point began to accelerate. 56. respectively. The finite element mesh and the von Mises stress distribution in the blade is shown in Fig. However. The stress intensity factor results were then input into the integration for crack advancement based on the Paris-law of the material. the stress distribution would have an effect. Fig. and then began to decline. 54. The arrow indicates where a crack would form. The crack depth increased monotonically. 54). 55.93. When the crack was small. which then drove the crack to grow faster in the surface length direction. 57. The crack depth and aspect ratio as functions of the cycle number normalized to its failure are shown in Fig. Since the stresses were relatively high at the notch root surface.2 Turbine Blade Crack Growth Next we consider a turbine blade that experienced premature failure due to fatigue crack growth. The principal stress over a quarter of the fir-tree root plane is shown in Fig. when the crack became large. The variations of the stress intensity factors at both the surface and the deepest points are shown in Fig. A finite element model was created for the blade and the stress analysis was conducted with the consideration of centrifugal loading and the blade contact with the disc. reached a constant value of 0. the stress over the crack was almost constant. the maximum stress intensity factor of the semi-elliptical crack occurred at the deepest crack front. 54. An initial crack of semi-elliptical shape exited in the trough of the first serration on the pressure side (indicated by the arrow in Fig. This change reflected the fracture mechanics characteristic of the elliptical crack and the effect of stress distribution on the cracking plane in the component. The a) initial and b) final crack profiles as revealed by post-mortem examination of the fracture surface are shown in Fig. Eq. The crack aspect ratio increased initially. .274 Gas Turbines 6. 58 (a) and (b). (73-74) with appropriate boundary correction factors. 56. The arrow indicates where the initial crack existed. 55. Crack depth and aspect ratio as functions of the number of cycles. Fig.Life Prediction of Gas Turbine Materials 275 Fig. Stress distribution (in unit of MPa) over a quarter of the fir-tree root plane (in unit of mm). . a) The initial crack profile. . and b) the final crack profile. 58. 57. Stress intensity factors at the surface and the deepest points. (a) (b) Fig.276 Gas Turbines Fig. R. M. UK. Trans. As regards to damage accumulation in the form of crack nucleation and propagation. Vol. & Harrison. G.. for creep-fatigue interaction. PA. addressing a variety of failure modes under high temperature loading conditions. Overall. Dwell sensitive fatigue in a near alpha titanium alloy at ambient temperature. a framework of integrated creep-fatigue (ICF) constitutive modelling is presented. Similarly. creep/dwell-fatigue interaction is nonlinear in nature. it offers an integrated methodology for life prediction of gas turbine components. T. a physics-based holistic lifing approach has been developed. Baik. S.M. The Metallurgical Society. Evans W. Advances in Fracture Research.. (1982). Particularly. the decomposition rule founds the physical base to relate transgranular (fatigue) fracture to ID and intergranular cavitation (creep) damage to GBS for polycrystalline materials. M. pp. the damage accumulation is related to grain boundary sliding. the damage is envisaged as dislocation pile-up. (1985). a general thermomechanical fatigue (TMF) model has been developed that involves creep-fatigue and oxidation-fatigue interactions. Ashby. 8. and a creep crack growth equation based on grain boundary sliding with stress relaxation ahead of the crack tip. . FL. H. The model has been shown to successfully correlate both “cold” dwell-fatigue and “hot” creep-fatigue.Life Prediction of Gas Turbine Materials 277 7. Fracture Mechanics: Fundamentals and Applications. Taylor & Francis Group. Development of damage tolerant microstructure in Udimet 720. 9 (eds. The TMF damage accumulation model physically depicts the process of fatigue crack nucleation and propagation in coalescence with the creep/dwell damages (cavities or wedge cracks) distributed along its path inside the material. 19.). pp. (1988). (1997). 3rd Ed. 13-22. R. B. M.H. Gambone. J. grain boundary precipitates and intragranular precipitates) dependence of the deformation behaviour with respect to each deformation mechanism. & Thoms.L. grain boundary morphology. K. 13A. Oxford. Crack growth in creep-fatigue is also described within the same framework in association with fracture mechanics.. 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Turbine blades of aircraft engines stand as a perfect example of components working in such a severe environment. 1Czech Republic 2Slovak Republic 1. From the point of view of corrosive and oxidizing effects. 2004). These components must withstand such a complex loading for a required performance and lifetime. quantitative approaches based on fracture mechanics can be used to assess the damage due to crack initiation and growth. Introduction Many structural components operate in very severe environments characterized by a high temperature. They are often made from layered material systems in which interfaces between layers play a key role for a prediction of durability. These surface barriers insulate the underlying substrate from the heat flux of gases. thermo-mechanical stresses and a presence of oxidizing and corrosive atmosphere. the properties can be controlled and balanced for a specific application.10 Damage and Performance Assessment of Protective Coatings on Turbine Blades Jaroslav Pokluda1 and Marta Kianicová2 2Alexander 1Brno University of Technology. Temperature patterns of incoming gases are inhomogeneous and. Diffusion aluminide coatings (DAC) are based on the intermetallic compound β-NiAl that forms under the influence of the substrate (usually Ni superalloys). Ta. they can be divided into two categories: diffusion and overlay coatings. In the MCrAlX alloy system. the composition of the overlay coatings MCrAlX remains independent of the substrate alloy.. etc. Hf. In addition. their temperature can increase in about 500 °C during a few seconds (Eskner. They are the most loaded parts of the engine owing to the high working temperature and mechanical stresses induced by forces and moments. 2007). Brno. thus contributing to an improvement of the engine performance. The metallic coatings on blades serve as physical barriers between the underlying substrate and the outer environment. an impact of hard particles can cause failure by erosion mechanisms. Fe (or a combination of these) and X means Y. On the other hand. Therefore. due to transient regimes. Each layer has different thermal and mechanical properties. Structural materials of rotor blades and their coatings determine a maximal permissible temperature of gases incoming to the high pressure turbine. only centrifugal forces acting on each blade can reach several tens of kN. where M means Ni. Si. increasing temperature gradients. Dubcek University of Trencin. Thermal barrier coatings (TBCs) are composed of ceramics and represent another group of so-called multilayered coatings. Trencin. this mode will not be discussed in more details. (ii) the aluminum containing bond coat (BC) located between the substrate and the TBC and (iii) the TGO which forms at the TBC/BC interface by reaction with the combustion gas. 2002). in columnar microstructures.284 Gas Turbines typically of yttria-stabilized zirconia (YSZ). sometimes.1 High-temperature oxidation Metals and alloys exposed to oxygen or oxygen-containing gases at elevated temperatures convert some or all the metallic elements into their oxides. if they remain adherent and form thermally grown oxides (TGOs) on the top of metallic coatings by reaction with the hot gases. TGO serves as a diffusion barrier to the next oxidation and. However. Up to now. also mentioned as an independent degradation mode. In general. In addition. the TBC must (Tamarin. from this point of view. The oxides can create a protective phase. The protective role of compounds such as Al2O3. oxidation and erosion provided the following requirements are satisfied (Nicholls. Degradation mechanisms of protective coatings Protective coatings used on turbine blades were developed to serve as physical barriers between aggressive environment and the substrate. • Creep degradation during overheating. • Interface stability. The efficiency of the thermal barrier systems depends on their heat conductivity and strain-tolerance. the oxidation cannot be considered to be a degradation mode. The coatings deposited on rotor turbine blades provide an optimal protect in the range of specified lifetime against destructive effects of high-temperature corrosion. • Damage by thermal and thermo-mechanical fatigue. Cr2O3 and SiO2 is to be particularly mentioned. retard creep degradation and reduce the severity of thermal gradients. • Good adhesion. 1996). 2000): • High oxidation and corrosion resistance. • Mechanical strength. In addition to these requirements to metal coatings. 2002): • Ensure lower average wall temperatures in cooled blades. • Hot corrosion. however. Here. this technology raises the thermal conductivity of the barrier. 2. • To level the temperature over the blade surface and reduce thermal stresses during engine transient running. Cr2O3 reveals to be most protective below 871 °C while . by layering of the ceramic within each column (Tamarin. For this reason the advanced technologies attempt to optimize both these crucial properties. The heat conductivity should be very low and can be improved by alloying of the ceramics or. TBCs are used as thermal barriers. The most serious degradation modes are as follows: • High-temperature oxidation. no coating that would fully survive the aggressive turbine environment has been found (Committee on coatings. The strain-tolerance becomes excellent when the deposition of ceramics is performed using electron-beam physical vapor (EB-PVD). 2. • Mechanical damage by erosion. Inter-diffusion of elements at the interface with the substrate that results in a creation of undesirable phases is. A protective scale can be maintained when the aluminum. but they are much smaller. Generally. PBR << 1 means that the oxide is porous and. PBR > 1 means that the oxide scale is highly compressed thus resulting in buckling and spallation (Bose. Residual compressions in the TGO reach up to 36 GPa as the system cools to ambient. both the coating and the substrate are environmentally exposed to a rapid deterioration of their microstructure. at temperatures above ~ 1000 °C. The scale becomes fully protective when PBR ~ 1. In order to form adequate thicknesses of Al2O3 in a reasonable time. A general indicator of the protectiveness of the oxide scale is given by the Pilling-Bedworth Ratio (PBR). At the same time. while the rate of this consumption is temperature dependent. only a modest oxidation of metals has been observed due to high protective properties of oxides forming on their surfaces. 2001b. In the temperature range (900 – 1000) °C. looses any protective properties. Logarithmic growth: x=k t x = x0 + kt (1) (2) x = k0 + log ( kt + 1 ) . 4-5 of weight % for Al (Committee on coatings. 2007). 2002): . diffusion of oxygen into the coating. which is defined by the volume ratio oxide formed/metal consumed. k is the temperature-dependent constant and x0 and k0 are constants. Elements as yttrium or hafnium are added to coatings to improve an adherence of aluminum or chromium scales to the substrate. the mechanism of oxidation can be explained by a consumption of certain elements to form protective scales. 2007): i.. The aluminum reserve in a defined zone of the coating can be found from the following function (Tamarin. (3) Here x is the oxide scale thickness after the time exposure t.Damage and Performance Assessment of Protective Coatings on Turbine Blades 285 Al2O3 protects at all temperatures up to the melting point of the blade alloy (Donachie & Donachie. 1998).e.. Coatings of turbine blades are oxidized during high-temperature cycles of engine running.g. 2002). chromium or silicon do not fall below their critical levels. Linear growth: iii. Tolpygo & Clarke. e. the diffusion processes between the coating and the substrate speed up thus resulting in a reduction of aluminum and chromium contents. generally less than 1 GPa (Evans et al. consequently. Parabolic growth: ii. i. When the oxide layer is eroded by hot gases or rubbed accidentally by removing the oxide layer. The metal coating serves as a reservoir of Al and Cr and amounts of these elements enter into life-time criteria. The adherent oxide scale also protects the metal surface from erosion. Additional necessary condition to form the protective scale is a close match of coefficients of thermal expansion (CTE). however. 1996). Disruption and spallation of the protective scale are exacerbated by a presence of impurities (mainly sulfur) on the metal/TGO interface. the catastrophic oxidation of the substrate can appear if the operation is continued at lower temperatures that do not allow a rapid recovery of the protective layer. The oxide scale growth in isothermal oxidation follows one of the following relationships (Bose. However. Stresses also arise during the growth of TGO.. A rapid spallation of TGO can be also caused by internal oxidation. Without the protective oxides. Oxide scales have lower CTE than those of the underlying metals and this difference generates large stresses. sufficiently high temperatures are required. the rate of coating oxidation raises. 2. Corrosive deposits can also seriously erode moving engine parts. 2001): i. These constituents usually originate from engine fuel impurities. reproduced with permission. i =1 n Gas Turbines (4) where mAl is the aluminum mass fraction. molten salts like alkali and alkaline earth sulfates. the temperature cycles. 2002). Hot corrosion is a chemical reaction between the metal and molten salts in the hot oxidizing flow.286 mAl = K ∑ Xi ρ i hi . the thermomechanical loading. marked as the type I or the high temperature hot corrosion (HTHC). Their interactions with materials cause corrosion and erosion.2 Hot corrosion At high temperatures. Solid particles can be molten by their transit through the flux of heat gases. SO2. Pit corrosion. the velocity and the composition of gas and erosion objects (Eliaz et al. Generally. ii. Types of the hot corrosion in terms of the metal loss as a function of temperature (Bose. clogging the passages and reducing or eliminating the cooling airflow. 1. The term “hot corrosion” distinguishes it from the traditional low-temperature corrosion. hi is the zone thickness and k is the alloying factor. contaminants of incoming air or products of imperfect combustion. marked as the type II or the low temperature hot corrosion (LTHC). Uniform corrosion. An intermediate zone mixed from both the oxides and the matrix can be also found between these basic layers. depleted of γ´ phase. chlorides and solid particles in the form of sand and fly ashes.V. Fig. Copyright 2007 by Elsevier B. 1) (Rapp. HTHC starts with condensation of fused alkali metal salts on the surface and its microstructure consists of an outer porous oxide layer and an inner zone. thus reducing the engine efficiency. increasing blade and vane operating temperatures and shortening the engine life (NASA. High temperature Coatings. that contains discrete sulphide precipitates. Salts in the form of gas have not a heavy corrosion effect but both the working process and the gas turbine environment lead to a formation of molten and solid compounds. the structures of engine turbines are exposed not only to oxygen but also to other constituents in the form of gas such as CO2. including the compressor and turbine blades. 2003). two modes of hot corrosion have been recognized (Fig.. These forms may be affected by various conditions including the alloy composition. A very small . Molten salts can solidify inside cooling passages. the composition of contaminants and the flux rate. 2007). ρi is the density of the zone. The BC at high temperatures is relatively soft and. This process is marked as “roughening” or “ratcheting” and may lead to local separations at . At ambient. High temperature gradients between the gas flux and the surface of cooled blades help the condensation of aggressive corrosion products which penetrate deeply into the coating and its substrate.. 2004). the compressive stresses are in the range σ TGO ∈ ( −3. During repeated startups. During the thermo-mechanical fatigue. Both the magnitude and the sign of these displacements are governed by mechanical properties of BC and TBC. In the case when rumpling of TGO occurs. as evident in Fig.1 The stresses in the TGO The stresses in the TGO exert a central effect on a failure of the TBC multilayered thermal protection system. 2.Damage and Performance Assessment of Protective Coatings on Turbine Blades 287 amount of vanadium might be detected in these corrosion products. Because of a low thermal expansion coefficient of TGO. the thin TGO layer (3 . depending on the thermal expansion misfit (Evans. 2007). 5. LTHC means a selective surface attack in the form of corrosion pits that form under longterm operation cycles at lower temperatures (around 700 – 750 °C). 2008). 2006). The coatings of blades are exposed to thermo-mechanical fatigue under cyclic changes near their ductile/brittle transition temperature (DBTT) that depends of their composition. Both stresses can be alleviated by the TGO creep and redistributed in the vicinity of imperfections. The high temperature has a major effect since it changes the chemical composition. −6 ) GPa .10 weight % and a small amount of sulphur (up to 1 weight %) (Tamarin. The analysis of the chemical composition of individual corrosion products revealed the presence of vanadium of 5 . load changes and shutdown operations. the compressive stresses are reduced.10 μm) seeks mechanisms to relieve the compression by means of out-of-plane displacements.3. 2002). the high-temperature components of the aircraft engine experience the thermal-induced strains and stresses that cause the thermo-mechanical fatigue (TMF) damage (Huang. consequently. fluidity and thermodynamic properties of corrosion products. 2. The research of engine operating conditions has proved that the higher the gas-flux velocity the slower the pit corrosion damage. Both the type I and the type II of hot corrosion retard the formation of protective oxides. they can be also modified by thermal cycling that causes a cyclic plasticity of BC.3 Damage by thermal and thermo-mechanical fatigue Thermo-mechanical fatigue is a degradation mode which involves simultaneous occurrence of both the thermal and the mechanical strain. 2001b). a large in-plane compressive stresses can develop upon cooling. Elevated temperatures along with high compression and flow rates in the turbine are the main reasons for the formation of a uniform HTHC region. They exhibit a ductile behavior and low strength at high temperatures while a brittle behavior and high strength is observed below the DBTT (Bose. 2. the displacements proceed predominately into the BC. It was found that fine-grained MCrAlX coatings undergo a typical transition in their mechanical behavior as a function of temperature. There are two main sources of these stresses: one from the thermal expansion misfit upon cooling and the other one from the TGO growth (Evans. different failure mechanisms operate below and above the DBTT. (Tolpygo et al. During the growth under influence of lateral compressive stresses. thus promoting the internal oxidation and sulphidation of the substrate and its coating. when the TGO remains planar without rumpling. the stresses can be expressed as σ ij σ0 h⎞A ⎛ = H ij ⎜ α D . Shear stresses σx'z' are induced at inclined sections (see Fig. The scheme of the stress redistribution on the interface. 2004).V. Fig. h/L<<1. i. Imperfections of the TGO and redistribution of stresses at the interface are evident in the schematic picture. reproduced with permission. Surface and Coating Technology.e. σ0 is the compressive stress in the oxide σ0 = E1ΔαΔT . Clarke & Murphy.. L⎠ L ⎝ (5) where σij are the stress-tensor components (i. where the tensile stresses σzz develop at the concave site of TGO while the compressive stresses σzz appear at the convex site. Fig. Vol. j = 1.. 3). Copyright 2004 by Elsevier B. 1 − υ1 (6) Δα is the difference in thermal expansion coefficient between the TGO and BC and ΔT is the amplitude of the temperature change (He et al. 2.j depends on the Dundurs´parameter . 188-189. 3. The microstructure of TBC/TGO interface separation after thermal cycling at 1150 °C (Tolpygo. 1998). When the TGO is thin relative to both the amplitude A and the wavelength L.288 Gas Turbines the interface TBC/TGO. The function Hi. 2. ⎟ . The magnitude and the sign of stresses depend on both the elastic modulus mismatch and the ratio of the amplitude A to the wavelength L. 3.). Distribution of stresses on the BC/TGO interface (Evans.3. i. Components of the turbine engines are protected from the aggressive environment by thin coatings. 1992). the main effort was devoted to numerical solutions for typical crack configurations in the substrate-coating systems.5 is plotted in the Fig. 2001a). Therefore.1 0. the energy approach demands information about a pre-existing crack configuration. However. (8) In the case of real structures with finite dimensions.0 -1. In these layered materials. size and orientation in the structure. Stress.3 0. reproduced with permission 2. G < Γ (Suo.2 Main design approaches to failure of thin layers Nowadays. the higher the values of stress components (Hutchinson & Suo.. Copyright 2001 by Elsevier B. The thicker is the TGO (the larger the ratio h/L).e.3 and 0. 0.e. for a pre-existing crack of a length 2a in infinite elastic solid subjected to a tensile stress σ. x/L Fig.. (7) Ei is the plane-strain Young´s modulus of elasticity ( Ei ≡ Ei in plane stress) 1 − ν i2 and subscripts 1 and 2 refer to the materials creating interface. σmax < S. i. such information is practically impossible to be obtained for real structures as integrated circuits or structures protected by various types of thin coatings.5 -1.1 0.2 σzz σx’z’ 0.1. 46.. geometry. two different design approaches to bulk structures are basically applied.5 0. 4.5 0 0.2.2001a).e.5 0. the interfaces are the most critical parts because of their .2 0.5 Distance.5 0 -0. 1993). Progress in Materials Science. If the maximum stress is lower than the material strength.4 0. 4.1 0. The stress approach is based on the measurement of strength characteristic S of the bulk material and calculation of the stress field in a real structure.V. The energy approach is based on the Griffith stability condition which means that the fracture toughness Γ of a cracked solid must be higher than the energy release rate G.Damage and Performance Assessment of Protective Coatings on Turbine Blades 289 αD = where Ei ≡ E1 − E 2 E1 + E 2 .3 0. i. Thus. 0. the following condition of crack stability must be fulfilled: πσ 2 a E <Γ. the structure is considered to be safe. The redistribution of the normal (shear) stresses σzz (σx’z’) for particular ratios h/L = 1 and A/h = 0. (Evans. Hij≡(σ ij/σ 0)(L/A) h/L=1 A/h=0. Vol. its location. αs. αs. therefore. In general. Γs) and (Ef. vf Substrate Es. The difference in elastic moduli is characterized by Dundur´s parameters αD and βD. αf. While the opening mode I is usually assumed to be a proper loading mode for the crack growing in the substrate or the layer. (10) The general relation (10) shows that the crack stability can be improved by reducing strain or residual stresses in the coating. 5. Scheme of the system substrate/coating heterogeneity. (7). Let us consider a thin film h on a thick substrate according to the scheme in Fig.290 Gas Turbines h σ Coating Ef. different thermal and elastic characteristics and presence of residual stresses. with elastic moduli. respectively. we will start with the stability assessment for a crack configuration within a thin layer. lowering the coating thickness.3. raising the fracture . Both the substrate and the film are assumed to be isotropic and linearly elastic.0 ) is the dimensionless factor depending on both elastic moduli and geometrical parameters of the crack configuration and Ef is the Young modulus of the layer (Hutchinson & Suo. Failure of these systems can be. the material constant Γ represents energy necessary for creating a crack of a unit area in the layer. ) (9) When combining eqs. 4. The parameter αD. predicted using elastic fracture mechanics. vs Fig. νf. The relatively simplest analysis can be done in the case of a very thick substrate and thin coatings in which an extent of plastic processes can be neglected. thermal expansion coefficients and fracture toughness (Es. in principle. Ef ( ) (8a) where Ω ∈ ( 0. νs. Γf). The latter case is rather complicated and. 5. substrate or at their interface. the mixed mode I+II must be considered for the crack propagating along (or towards) an interface. (8a) and (9) along with the condition G<Γ one obtains 2 Γ f > Ωhε T E f . The layer is stiffer (softer) than the substrate when αD > 0 (αD < 0). Here the energy released rate reads G= 2 Ωhσ 0 1 −ν f . αf. 1992). as defined by eq. is a measure of incompatibility between the Young´s moduli whereas the parameter βD measures the difference in bulk moduli. The strain induced by cooling from a high temperature T0 to the ambient temperature TT due to a contraction difference can be expressed as σ0 = Ef 1 −ν f εT = Ef 1 −ν f (α f − α s (T0 − TT ) . due to formation of volume-inconsistent Y2O3 phases. the critical coating thickness still ensuring the crack stability is determined as follows: hc = Γf 2 Ωε T E f _ . iii.min . According to (Wang & Evans. subjected to a particular stress.m−2 .4 ) i μm.m-2) are usually associated with a segregation of i impurities (mostly sulphur) on the TGO/substrate interface. 1992). A very tough TGO/substrate interface of ΓO ≈ 20 J. ΓO is the fracture toughness of the interface for the i i opening loading mode. Unbalanced diffusion fluxes create a high concentration of vacancies that produce microvoids. Thickness values of this range are an order of magnitude smaller than those of real TGO separates (Hutchinson & Suo. On the other hand. the critical value of the biaxial compressive stress σb. separate the oxide layer from the substrate. 1999).c = ξ h f . (11). Buckling of the separated TGO segment and further growing of the related interface crack. Consequently.m-2 manifests itself by internal cracking of TGO. When using typical i values E f = ( 350 − 400 ) MPa . • Rippling of the TGO/substrate interface induces tensile stresses that.c can be. Buckling of the TGO layer When a symmetric circular separate. Lower values of ΓO (≈ 5 J. Partial separation of the TGO segment from the substrate This failure mode can be caused by the following processes: • Void coalescence on the interface as a result of non-equilibrium diffusion fluxes of metallic ions during the through-boundary oxidation. expressed as h f .1.3.3 Failure modes of TGO Cracking initiates predominantly within the TGO/substrate interface and proceeds by a small-scale buckling of the TGO layer (Wang & Evans. e.0. σ 0 = ( 3 − 4 ) GPa and ΓO = 5 J . where Ω ≈ 1 and Γ f → ΓO . reaches a critical radius bb it expands to create a buckle. in most cases. one obtains h f . ii. A minimal thickness of the TGO layer hf. • Thickness variations during an imperfect growth of TGO.Damage and Performance Assessment of Protective Coatings on Turbine Blades 291 toughness Γf and utilizing more compliant materials.min below which no separation occurs is defined by eq. (11) 2. assisted by voids and inclusions. Spalling of the TGO segment. Partial separation of TGO from the substrate that initiates at interface inhomogeneities.c for buckling of the circular TGO separate can be expressed as . (12) where ξ > 1. the critical thickness for TGO failure hf. This process consists of the following stages: i.g. • Creep and grain-boundary sliding in the substrate leading to decohesion of the oxide film from the substrate.min ∈ ( 0. 1999).. c . i.). which is caused by tensile stresses that are induced on the real rippled interfaces.22 is the so-called critical index of buckling.c and b) bs. f (17) kink bb. Spallation of the TGO layer Deflection (kinking) of the crack from the interface towards the TGO interior appears in consistence with a criterion taking both the loading mode and the ratio ΓO Γ f into account i (Hutchinson & Suo. G ≥ Γ i . Since the buckle can extend under general mixed mode I+II.292 Gas Turbines σ b . 1992). λ = 0 to a rough surface). The plot of the function f (ψ ) can be found in (Hutchinson & Suo. where bs. the critical buckling radius bb . the value of Γ i depends on a particular crack-tip loading mode: Γ i (ψ ) = ΓO f (ψ ) . ΓO Γ f > 0.e. i. Kinked cracks at the radii: a) bb. If the fracture toughness of the interface is sufficiently high.c a) Fig. the kinking appears before the onset of crack extension (Wang & Evans.c ≈ 50 μ m . The buckled separate starts to extend when the energy release rate G exceeds the interface fracture toughness Γ i . KI and KII are the stress intensity factors in modes I and II and λ is the coefficient depending of the interface roughness (λ =1 corresponds to a smooth surface. i (14) (15) (16) f (ψ ) = 1 + tg 2 ⎡( 1 − λ )ψ ⎤ .c = Π c Ef 1 −ν f 2 ⎛ hf ⎜ ⎜b ⎝ b ⎞ ⎟ .c = ϕ * ( 1 −ν ) h f E f ΓO i . When assuming only dilatation-induced compressive stress on the TGO/substrate interface σ 0 ≈3. 6. ⎟ ⎠ 2 (13) where hf is the TGO thickness and Π c = 1. KI where ψ is the loading phase angle.6. 1992). b) . 6a..5 GPa (hf = 5 μm).c. i which means that bs .This value is much higher than the real one. ⎣ ⎦ ψ = tg −1 K II . 1998). The critical stress for the spallation of the buckled TGO segment is given by the relation σ s .e.c is the critical radius of spallation (Fig.c = bb .c kink bs. 1998). In this range. Creation of continuous cracking demands a development of a critical TGO thickness as YSZ 2 π 1 − ν 2 md 2 KTc hc = ( m − 1) REYSZ ( ) 3 . 25 ⎥ . the TGO/BC interface embrittles due to segregation of impurities (mainly S) that reduce its adhesion strength and fracture toughness ΓO (Evans et al. Moreover.c hf where =χ Ef . many such cracks must coalesce (Rabiei & Evans. 1992). thus prohibiting its separation. Since the cracks emanating from individual imperfections are too small to satisfy large-scale buckling conditions. the buckle is extended i along the interface before its spallation by reaching the critical radius bs.7 (He et al. 7b. (20) . 6b. The TGO imperfections are crucial for the life span of TBC systems also because of tensile hoop stresses σzz. the ratio of the critical length bs. Initiation and extension of this degradation mode operating i on the BC/TGO interface can be assessed by using so-called spallation maps that identify regions of individual damage stages (Wang & Evans. the critical parameters that control both the extension and the spallation of the TGO separate are σo.. This stimulates extension of separates in the vicinity of i coarsed and/or rippled TGO segments. At high temperatures.c (Fig. the damage proceeds by creating a large scale buckling (LSB) that develops on the interface after reaching a critical size. the thermal expansion misfit induces tensile stresses normal to the TGO/BC interface thus inducing its separation.3. the cracks remain confined to the TBC during exposure. Consequently. Therefore.). ⎥ ⎦ (19) Thus.1exp ⎢0. 2000). the TGO layer remains brittle and the hoop tensions are not replaced by compression related to the thermal expansion misfit..4 Failure modes of TBC Mechanism of TBC degradation assisted by heterogeneities The presence of the thermal barrier suppresses the small buckles. According to (Hutchinson & Suo. In the case of lower values ΓO Γ f . 1999).) which is surmised to happen upon cycling in the range of intermediate temperatures. hf. A mutual coalescence of interface and radial cracks is a key event of the TBC degradation (Fig. When cooling to ambient. 2. 1999). (18) σo χ ≈ 1. During the thermal exposure. ΓO and Γ f .Damage and Performance Assessment of Protective Coatings on Turbine Blades 293 where ϕ * ≈ 1. the TGO/bond-coat interface is in compression. however.7 ⎢ ⎣ ⎡ Γf ΓO i ⎤ − 1. these cracks do not penetrate the TGO since the ductility of this layer causes a redistribution of stresses at their inner front. perpendicular to the YSZ/TGO interface that are induced in their proximity and initiate radial cracks within the TBC layer.c and the thickness hf can be expressed as bs . d is the half-spacing of two adjacent heterogeneities. This cracking leads to the spallation (as already mentioned for LSB) or to the edge cracking. Cracking of TBC due to cyclic plastic deformation and decohesion of the TBC/TGO interface (Tolpygo & Clarke. In the case of planar TGO. 2001b). as documented in Fig. 8. on the other hand. Vol. both the high R and the small d of ripples at the TGO/bond-coat interface increase the probability of continuous cracking inside the thermal-barrier coatings. The related tensile strains εzz and stresses σzz in the YSZ layer nucleate cracks parallel to the interface according to the scheme in Fig. Copyright 2000 by Elsevier B. the absence of shear stresses in the substrate (except for free edges) means that there are no out-of-plane displacements as reactions on the thermal cycling (Evans et al.. 1999).V.. consequently. reproduced with permission where m is the volume ratio of newly created TGO to exhausted BC (m = 1 for no volume YSZ changes). reproduced with permission Degradation of TBC by penetration of sulphide sediments and air sands YSZ layers utilized for burning parts of aircraft engines are subjected to temperature gradients developing in the course of service. the shear stresses in the substrate can exceed yield stress and. KTc is the fracture toughness of YSZ for short cracks (a ≤ 100 µm) under mode I and R is the radius of a circular heterogeneity (Evans et al.. Copyright 2000 by Elsevier B.V. Vol. the amplitude of the rippling raises by plastic deformations of the substrate. a) Radial cracks induced in the TBC.. 2000). b) Coalescence of radial cracks with the interface separation caused by TGO growth and followed by cooling to ambient (Evans et al. Recent investigations and monitoring of real . Thus. When the TGO becomes rippled. 48... 48. 7. 7. 8. 2000). Acta Materialia. Acta Materialia. These ripples are formed by the ratcheting process under thermal cycling that relaxes compressive residual stresses within coatings (He et al.294 Gas Turbines a) b) Fig. 2003). Fig.. 2008): • Zone I – superficial penetration of CMAS. 2005). MgO. Scheme of cracks at levels (i) and (ii) inside the zone III. 1996).5. When the temperature of the TBC surface exceeds the melting temperature TmCMAS ≈ 1240 °C of CMAS compounds. The sand CMAS particles damage the turbine blades particularly in aircrafts flying at lower altitudes over arenaceous regions. .Damage and Performance Assessment of Protective Coatings on Turbine Blades 295 components from the burning parts of turbines reveal that the YSZ coatings are susceptible to damage in sites of a dense microstructure (Borom et al. Further cooling results in accumulation of elastic energy at the level (ii) that is high enough to form and propagate mode I cracks in the direction parallel to the surface. These very small particles (smaller than 10 μm) do not posses a sufficient kinetic energy to cause the impact damage (Strangman et al. When the ratio of the penetration depth h to the total thickness H of the YSZ layer reaches h/H ≈ 0. Al2O3) and/or sulfides but also by sintering of the layer fringe. After cooling... Later on.. 9. 1996). the elastic energy accumulated in the zone III.. it draws in the spaces of columnar oxides to a depth where TTBC = TmCMAS . the CMAS layer starts to melt. The damage by sulfides is typical for components exposed to a seaside atmosphere.). bedraggle the YSZ and. the total volume remains identical with the original one. a release of yttrium from the YSZ can cause its transformation from the tetragonal to the monoclinic structure (Borom et al.2 mm. Zone II – intermediate penetration of CMAS: damage is similar to that in the zone I but • the surface is smoother. Damage of the coating can be particularly identified inside three zones (Krämer et al. Channel crack σxx σxx CMAS penetrated layer Level (ii) Level (i) h H YSZ Bond coat Fig. the CMAS layer hardens and forms a fully dense phase which thermomechanical properties increase its tendency to spalling (Mercer et al. such dense layers can be formed not only by penetration of calcium-magnesium-alumino-silicate (CMAS) particles (CaO. 2007). The YSZ volume containing the penetrated coat has a higher elasticity modulus and. the spacing of which is about 0. 9. With regard to the environment in the turbines. Regions penetrated by CMAS phase are also detrimental due to a reduction of thermal conductivity of the TBC barrier. the cooling from high temperatures induces surface tensile stresses that drive the cracked channels to grow throughout the TBC layer. at the same time. by action of capillary forces. however. SiO2. the densified region contains a number of dense vertically cracked (DVC) system. • Zone III – depth penetration of CMAS: an extended infiltration of CMAS results in a network of long vertical cracks close to the bond coat (see Fig. Because of a very thin CMAS layer on the surface. again. such a high velocity can also be reached with a help of the rotation motion of the runner. 2. the stresses are controlled by elastic waves. induced by elastic waves.4. the main damage process of thermal barrier coatings.3 Impact of large particle with high kinetic energy When a large particle impacts on the surface at a high temperature. Thus. to velocities as high as 200 m..296 Gas Turbines level (i). Starting with the application of EB-PVD depositions. Such an elastic impact induces zones of local tensile stresses in the surface region close to the impact site.. these particles cause additional mechanical damage by impact and erosion.1000 μm. 11. Spallation of the coating due to both the TGO growth on the BC/TBC interface and the thermal mismatch stresses was. These stresses cause local bending of columns and initiate knocking off the column edges. 2004).2 Impact of medium-sized particle with mediate kinetic energy Such impacts usually create the so-called densified zone (DZ) which. 2. 2005). (Chen et al..1 Impact of small particle with low kinetic energy Impact of small particles on the surface of TBCs with columnar structure initiates short cracks that do not further propagate through the coating since the column boundaries act as growth inhibitors (Wellman et al.6 k 2 κΛ 3 . Subsequent impacts of particles form a thin DZ until tensile-stress concentrations induce a partial decohesion at the DZ/column interface. sized 10 . erosion and impact of hard particles became the most important damage processes in the case of TBC with a columnar structure. A schematic picture of this mechanism is shown in Fig. 2008). for a long time..4 Mechanical damage by erosion Mechanical damage of coatings may also be initiated by intrusion of foreign particles into the gas-air space of turbines at high operating temperatures that facilitate plastic deformations of thermal barriers. the major part of its kinetic energy is absorbed by plastic deformation and creation of DZ in a close proximity of . This critical depth can be expressed as * H pen = 3. In gas turbines.4.4. however. 2004). becomes sufficient to drive the cracks from deep channels in mixed mode over the * bond coat. 2008).. These stresses are.. (21) where k is the coefficient of thermal conductivity of the penetrated layer. 10. the formation of dense plastic surface layer is impossible and the columns remain separated. Particularly in the case of a low kinetic energy and temperature. This means that there must be a critical penetration depth H pen below which no cracking of TBC coating appears (Krämer et al. Mechanism of such a damage is schematically depicted in Fig. κ is the coefficient of heat transfer on the TBC surface and Λ ≈ 800 is the material constant (Mercer et al. 2005). 2. (Chen et al. 2. Because such impact processes are of a very short-term character (~ 10 ns). Working conditions and the turbine environment can speed the oxide particles. Further impacts rebuild the DZ during the time span of 1 ms. is too thin to cause damage high enough to delaminate the TBC/TGO interface.s-1 (Crowel et al. Scheme of damage processes associated with an impact of a small particle (Chen at al. 2004). (Chen et al. 11... 256.V. parallel to the surface. reproduced with permission Fig. The particular damage mechanism depends on the size and velocity of particles.Damage and Performance Assessment of Protective Coatings on Turbine Blades 297 Fig.. temperature and material (Nicholls et al.V. 2004). A scheme of related damage mechanisms is shown in Fig. Copyright 2004 by Elsevier B. Plastic deformation within DZ might be accompanied by bands of columns that are inclined at nearly 45° from the surface and contain cracks.. Copyright 2004 by Elsevier B. 256.. 1998). The width of these bands is several times higher than that of the individual column (Crowell et al.. 2003). Wear. Scheme of damage processes associated with an impact of a medium-sized particle (Chen et al... the cracks grow along this boundary. 2008). Wear. 10. i. reproduced with permission the impact site. 12.e. Vol. . When the band reaches the TBC/TGO interface. Vol. melting down particularly the grain-boundary phases. 12. 2002). Alloy Rene 80 IN 100 MAR-M-200 B-1900 PWA 1480 CMSX-3 Melting temperature (°C) 1225 . a relative term since. 352.1330 1315 Solidus γ´ (°C) 1150 1180 1180 .V. ii.1230 1175 . Copyright 2002 by Elsevier B. The excessive temperature is. however.. Relevant melting temperatures are displayed in tab. Materials Science and Engineering. 2003). Scheme of damage processes associated with an impact of a large particle (Chen et al. 2002): i.1200 1150 - Table 1. Melting temperatures of cast Ni-alloys and strengthening γ´ phase .298 Gas Turbines Fig.1200 1260 1260 1315 . These effects are dependent of both the temperature level and the time span. Vol. extraordinary oxidation and corrosion. 1 for several Ni-based cast alloys (Donachie & Donachie.. Indeed. In general.5 Creep degradation after overheating Overheating means an exposure of a material to an excessive temperature during a short time. this could only lead to a partial reduction of materials strength and/or ductility. for some unloaded components. The melting of selected phases cannot be recovered by any heat treatment. any temperature should be considered as the overheating one when it has the following consequences (Donachie & Donachie. it need not necessarily cause serious problems. iii. dissolving of strengthening phases in the matrix. reproduced with permission 2. (Donachie & Donachie. 2003). 14. When the service temperature is reached. Ciesla & Swadzba.. (b) after overheating (Donachie & Donachie. 2009. burning outside the combustion chamber and human factors (Pokluda et al. Damage of air-cooled blade channels by creep deformation (Tawancy & Al-Hadrami. when the peak overheating temperature is nearly reached. The latter paper.Damage and Performance Assessment of Protective Coatings on Turbine Blades 299 Example of dissolving of grain-boundary phases after overheating associated by a reduction of creep strength is given in Fig. both the high heat conductivity and the low thickness of the diffusion layer eliminate the temperature gradient very quickly and. Analyses of specimens revealed numerous voids and microcracks at the grain boundaries of the substrate. During overheating and further thermal cycling in service. 13. however. 2008. 2010).. However. iv. Copyright 2002 by ASM International. 2003. 2003). Escalation of the working temperature by surging. Rangaraj & Kokini. the compressive stress again appears as a consequence of the coating/substrate temperature gradient (Rangaraj & Kokini.. Superalloys: a Technical Guide. reproduced with permission In practice. Because the thermal expansion coefficient of the coating αc is lower than that of the substrate αs. The tensile stress induced in the . iii. 2003). for example. the compressive stresses become substantially reduced also by the substrate/coating relaxation. the delay between the onset of the overheating and that of the tensile stress (the range t1 – t0) depends on the layer thickness and the heat conductivity of both the diffusion layer and the substrate. 2002. reports on the evaluation of damage of aluminium layers on the nickel base superalloy after short time creep tests. the high-temperature components as stator and rotor blades of aircraft turbines are damaged by overheating due to the following events: i. In general. wrong composition of the combustion fuel. Microstructure of a nickel-alloy: (a) before overheating. Intrusion of foreign particles into the engine. such defects can develop to cracking along and through the thickness of coatings (Tawancy & Al-Hadrami. This is schematically shown in Fig. the stress changes to a tensile one. A lot of papers deal with an effect of creep mechanisms on the degradation of superalloys with protective coatings (Tawancy & Al-Hadrami. Evans et al. During the first part of the overheating stage. 2009). damage of hot section components starts to be very extensive during a very short time and it is accompanied by plastic deformation and cracking particularly on the surface. 2008). (a) (b) Fig. 13. 2006). 2004). Insufficient filtration of the inlet a blocking of cooling channels by various contaminants (volcanic ash. 2005). the coating experiences compressive stresses after cooling down from the deposition temperature (Wang et al. (Pokluda & Kianicova. 2002). sands) that subsequently melt in the channels (Report NASA. ii. If the critical temperature of gases becomes higher than nominal. They experience a variety of loading during starts-up and shuts-down and undergo sudden changes of loading during flight manoeuvres. on their mechanical hysteresis and tendency to ratcheting (Wang et al. both the sign and the level of relatively low stresses in the coating are determined by thermal cycling around the service temperature (flight manoeuvres) and depend on the stress-strain response of both the coating and the substrate. Owing to surging. an overheating shock can appear so that the working temperature T of blowing gases exceeds its critical value Tc = 760 °C (Kianicová. Fig. 14. 2010).300 Gas Turbines coating steeply increases during the first stage of the cooling period and. During a further service. 2005). Scheme of the development of thermal stresses in the coating layer during the overheating process (Pokluda & Kianicova. Rotor blades of the high-pressure turbine are the most heavily loaded components of the runner wheel.).. The engine is appointed for light training combat aircrafts. The heating curve and the related timedependence of the thermal stresses are respectively plotted by the dashed and the full line. 14. for a certain period of time t3 – t2. an empirical degradation parameter is used as D = ( t2 − t0 )(Tmax − Tc ) 3 t2 t0 ∫ ⎡T ( t ) − Tc ⎤dt . retains its sign also after the termination of the overheating period (Fig. Engineering Failure Analysis (in print). The producer has to decide about their further performance till the next general repair on the basis of an extract of preceding overheating data.. Case study: assessment of performance capability of Al-Si coatings after overheating Motivation for this study came from a demand for a substantial extension of our knowledge about microstructural degradation of diffusion Al-Si coatings (AS layers) protecting rotor blades of the aircraft engine DV2 produced by HTC-AED a. ⎣ ⎦ (22) ..s. For that purpose.e. Považská Bystrica. Slovakia. i. where sudden changes of the engine output are in progress during flight maneuvers. reproduced with permission 3. Copyright 2010 by Elsevier B. 2006).V.. . T > Tc and Tmax is the maximal overheating temperature (HTC-AED. Copyright 2010 by Elsevier B.5x109 < D ≤ 1010 1010 < D≤ 1012 1012 < D ≤ 1014 1014 < D ≤ 2. They are designated for work temperatures in the range of 800 – 1050 °C.Damage and Performance Assessment of Protective Coatings on Turbine Blades 301 where t є < t0. 16. 2. Engineering Failure Analysis (in print). the producer meets a statement concerning the performance capability.s2] 105 < D ≤ 1. Substrate Inner zone Outer zone Fig. D [°C4. By means of that procedure and Tab. The degradation of the AS layer was analyzed for blades that were subjected to different overheating conditions during service (Pokluda et al. The procedure consists in the spraying of an equally balanced suspension of aluminum and silicon powders together with the coloxylin as a binder. The final microstructure of the layer consists of two sublayers. The protective coatings just after deposition.2x1014 Engine status Full performance capability (FPC) Degraded layer on rotor blades of the high-pressure turbine (DHB) Degraded basic material of rotor blades of the high-pressure turbine (DBM) Degraded blades of the low-pressure turbine (DLB) Degraded basic material of disks (DD) Melted blades (MB) Performance capability Operation Repair Repair Repair Repair Out of operation Table 2. Kianicová et al. 2007). reproduced with permission Polycrystalline rotor blades are made of nickel-based superalloy by a precise casting. 15. It was found that the relative thickness of the degraded surface layer was a monotonically decreasing function of the parameter D (Kianicová & Pokluda..5x109 1.V. the inner one contains aluminides of a lower Al-content and finely dispersed carbides and silicides. In the engine DV2 the blades of the high-pressure turbine are protected from high-temperature waste gases by using the heat-resistant AS layer. This is demonstrated in Fig. t2 > is the overheating duration. where the relative thickness hr = h/h0 of the diffusive . Assessment of performance capability of the aircraft engine in terms of the parameter D.2x1014 D > 2. 2009). Diffusive tempering is applied at 1000 °C in an inert argon atmosphere with the dwell time of 3 hours and subsequent slow cooling in the retort. 15.. 2010). The outer one is composed of mostly alloyed aluminides and a small amount of carbides. 1998). (Pokluda & Kianicova. 2008. see also Fig. One can see that the following quadratic relationships hrb = 1. reproduced with permission The value h0 ≈ 28 μm corresponds to the average initial thickness of the virgin layer. This means that the latter curve is crucial for the assessment of the damage level of the blade according to the benchmarks DHB and DBM given in Table 1. .23 (log D = 1) which is related to the maximum average thickness hmax ≈ 34 μm of the diffusive coating. The value hrt = 0.2540 − 0.2734 − 0. Engineering Failure Analysis (in print). Moreover. 14). Dependence of the relative thickness hr of the coating on the level of degradation in terms of the parameter D for n = 3. 2006).0055 ( log D ) hrt = 1. The points indicate the results of measurements performed on blades coming from four engines that experienced overheating of various intensities (see Pokluda et al. 2010). p = 1/4 and q = 3/4 (Pokluda & Kianicova. The parameter D possesses an interesting physical meaning. The solid curve stands for through whereas the dashed one for the back of the blade.0295log D − 0. 2010). Fig.0108 ( log D ) 2 (23a) (23b) 2 well approximate the reduction of the relative thickness on both the back (hrb) and the through (hrt) after the overheating events of various intensities. When assuming a creep work done by tensile misfit stresses during the overheating event (Fig.. 2008 for more detail). Thus.0141log D − 0. Such a thickness is achieved after several hours of service under a standard working temperature (Kianicová. the description of blade damage using the parameter D according to eq. Copyright 2010 by Elsevier B. 16.302 Gas Turbines protective layer on the back (convex side) and the trough (concave side) of the blade is plotted as a function of log D.21 related to the benchmark DDHB = 1. Both curves start at hr = hmax/h0 = 1. The damage curve for the back lies above that for the through. one can show that this parameter is directly proportional to the specific Hamiltonian´s action SE that contains a basic information about the evolution of damage in the system (Pokluda & Kianicova. the trough layer is totally removed when reaching the value hrt = 0 which exactly corresponds to the benchmark DDBM = 1010 °C4s2 indicating a start of the degradation of the basic material.. (22) seems to be very plausible.V.5⋅109 °C4s2 that indicates an onset of the range of the necessary repair seems to be very reasonable: 79% of the original through layer and 46% of the original back layer is already removed. researchers and designers with not only a deep insight into basic degradation micromechanisms of protective coatings. Nevertheless. need a further verification. (24). ⎣ ⎦ 2 4 (24) as a nearly equivalent to D could be found in this way. Repeated overheating of the engine. To justify a reliability of the parameter Dn would. ii. 2008). overlay and thermal barrier) on turbine blades of aircraft engines during service. (24) where p + q = 1 and n ∈ (1. this article provides scientists. The parameter D defined by eq. (22) represents a special case of eq. On the other hand. Most important material and design parameters of coatings are highlighted with respect to an optimum protection from damage caused by aggressive environment and thermo-mechanical loading. indeed.. these cases can be easily identified when analyzing records of the turbine revolutions and the overheating events during service (Pokluda et al. The assessment procedure based on the parameter D does not provide correct data in the following special cases (Kianicová et al. However. Although a special emphasize is devoted to destructive effects of thermo-mechanical fatigue and overheating. However. . (22) can. one can find 28 various possible combinations of these parameters. one cannot exclude the possibilty of other suitable forms of the damage parameter since various sets of parameters n . Thus. (24) for p = 1/4. q = 3/4 and n = 3. p = 1/4 and q = 3/4) can basically be considered as well. 2010). however. 2009): i. This article presents an overview of damage mechanisms leading to failure of all basic types of coatings (diffusion.Damage and Performance Assessment of Protective Coatings on Turbine Blades 303 Consequently. A simple method for an assessment of performance capability of diffusive coatings is presented as a case study performed on rotor blades of high-pressure turbines in aircraft engines. For this purpose. be considered to be the best of all these alternative damage indicators (Pokluda & Kianicova. a much simpler damage parameter Dn = ( t2 − t0 ) ⎡Tmax − Tc ⎤ . p and q (different from n = 3. Note that the value n = 3 indicates a plausible mixture of diffusion and dislocation damage mechanisms during the creep exposure. 4. Conclusion Protective coatings on blades serve as physical barriers between the underlying substrate and the outer environment. the related numerical analysis revealed that the parameter D as defined by eq..6) . the damage function can be expressed in more general form as SE ∝ D = ( t2 − t0 ) 1 + q − np q ( n + 1) ⎪ ⎡Tmax − Tc ⎤ ⎣ ⎦ ⎧t 2 ⎫ ⎪ ⎡ ⎤ ⎨ ∫ ⎣T ( t ) − Tc ⎦dt ⎬ ⎪ t0 ⎪ ⎩ ⎭ p ( n + 1) . The overheating is caused by a gas burning outside the combustion chamber which results in a sudden decrease of turbine revolutions. oxidation and erosion effects are also described. When retaining the physical meaning of D in terms of the unit (oCn+1s2 ) and avoiding both fractions and negative values of powers in eq. but also a practical example of engineering application. many recent results of advanced numerical models based on fracture mechanics are taken into account. the severe effects of hot corrosion. Vol. (1996) Role of environment deposits and operating surface temperature in spallation of air plasma sprayed thermal barrier coatings. 4903-4113. Coatings for Hightemperature Structural Materials. 116-126. G. Vol. C.H.A.. 245.G. Evans. pp. Bose.W. G. M. pp.Y. 1-2. Effects of morfology on the decohesion of compressed thin films. 4150-4159. Vol. Engineering Failure Analysis.W.. References Borom.. ISSN 1350-6307.W. Elsevier Science & Technology Books. Shemes. 31-43. 249-271. ISBN 0750682523. Vol.. Mumm. No. He. M. McMeeking. pp. No 1..W. (1999) Interface adhesion: Effects of plasticity and segregation. M. Acta Materialia.. A.9. A.A. C. M. (November 1999). 16. 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ISSN 1359-6454. Vol.. V.M. No. (2003d). because it comprises complex dynamical subsystems which can fail due to faults in sensors. To analyze under which conditions faults in sensors and actuators of a GT can be detected and isolated. The key for a faults diagnosis system is the discrepancy between expected and actual behavior and this can be identified. Universidad Nacional Autónoma de Mexico Instituto de Investigaciones Eléctricas México 1. (2003a). actuators and components and relies heavily on the control system affecting the reliability. considering diverse fault scenarios. However previous to the residual generators design it is necessary and essential to determine which data requirements are required to solve a specific fault diagnosis issue. the structural properties of the model are used here. The redundancy of the structure is studied using graph tools for the subsystems of the GT considering the available measurements. it is suggested here to add a sensor to increase the redundance and consequently to improve the fault detectability of the turbogenerator in the presence of mechanical and sensors faults. 10 relations are obtained which allow to detect faults in all components of the gas turbine unit. 1990). GT. 2008). This issue motivated this research work oriented to design a diagnosis system by software for gas turbines of electric power plants. availability and maintainability of the power plant. This is the main contribution of the work. Introduction This chapter deals with the fault diagnosis issues for a Gas Turbine. on real time only if redundant information between the process variables is available (Frank. Artificial Intelligence and Control communities have developed methods to generate symptoms or signals by software. called residuals. The rotors mechanical coupling to gas turbine unit for one side and the electric generator unit for the other side. the standard instrumentation of the GT restricts its performance from safety and integrity point of view. CCPP. (2003c). is identified as a subsystem in which faults are undetectable and then. The implementation of redundant graphs with specific simulated data of a GT validates this statement. On the base of this result and using the redundant graph concept (Verde & Mina. which reflect the discrepancies in faults conditions Venkatasubramanian et al. A non-linear complex dynamic model of the GT given by 37 algebraic and differential equations is considered to identify the required redundancy degrees for diverse fault scenarios of the units without numerical values. As result of the generic analysis. of a Combined Cycle Power Plant. The essential and more critical component in the plant self is the gas turbine. Venkatasubramanian et al. a diagnosis system for this subsystem is not feasible. Venkatasubramanian et al. Cristina Verde and Marino Sánchez-Parra .11 Application of Structural Analysis to Improve Fault Diagnosis in a Gas Turbine Instituto de Ingeniería. This means. As example. The second one introduces the structural framework to detect and isolate faults in a complex dynamic plant where the concept of redundancy graph is introduced. (1). 2006). Section 3 describes shortly the model structure of the GT and the interconnection between units used in the study. Therefore. This means. The general frameworks are described in the books (Korbicz et al. 2008). These scenarios determine the generic redundancy equations which have to be implemented in the supervision system of the GT. Section 4 discusses in detail the analysis of the GT by graph tools considering the feasible fault scenarios in sensor and actuators. The principle to solve a fault diagnosis problem is the redundancy and consistency of data in a system (Frank et al. In this framework a fault for the study case is defined as deviations of the GT from its normal characteristics affecting the automatic system (Isermann. the control theory. Following this analysis. This simple procedure generates delayed alarms without detailed diagnosis. the main contribution is given in first part of Section 5. if for all Ki consistent with the process free of faults.) = 0 (2) obtained from an analytical model is called an Analytical Redundancy Relation ARR for a set of detectable faults F. 2. 1999) together with model behavior in normal and fault condition. and if a fault fi ∈F occurs. one can estimate by software y.y) are known. Process supervision with fault diagnosis The automatic supervision of power plants was mainly realized in the past by limit checking of important process variables. ARR is inconsistent or different from zero at least in a time . Usually alarms are raised if the limit values are exceeded and protection systems act manually or automatic. where one way uses a mathematical model in analytical form (Blanke et al. the data of y gives a redundant information and one can check the system behavior looking for the dissimilarity between ŷ and y. Then. The second part of Section 5 includes some numerical results of the implementation of the detection system. The first part of Section 2 presents the philosophy behind an active supervision system by software. to determine variables of a process. Modern methods based of system theory made possible to develop advanced fault detection and active diagnosis systems by software (Venkatasubramanian et al. Based on the Redundant Graph RG.. called ŷ. 2003).. the subsystem without redundancy is here described and how to look for a new available variable in the graph to improve the detection capabilities and isolability properties of the turbogenerator unit. 2004). a model is not so simple as the above case. any expression of the form ARR(Ki ) = RR( ki . (Ding. given a vector ki integrated by a subset of known signals Ki of a process. For large scale systems. signals processing and artificial intelligence communities have proposed diverse methodologies to supervise the system behavior. The analytical formulation of a discrepancy assumes the existence of two or more ways.. To develop modern automatic supervision and diagnosis system a combination of diverse methods have been developed by the safe process community of IFAC. for the model y = 3u + 6u2 − 4uy (1) assuming that both variables (u. ARR is zero. 2003b). based on u and Eq. ki .308 Gas Turbines The work is organized as follows. and the discussions of the results and conclusions are given in Section 6.... ki . y ε ℜ ny (3) (4) (5) 0 p = m( x . (Korbicz et al. x . The following description formalizes this concept. f . So. one should select a method which captures all possible solutions of a diagnosis issue taking in account the available measurements. Geometric Approach (De-Persis & Isidori. The relations of class (2) can be obtained by different methodologies: analytical expressions. 2003). the next issues are formulated here: • Which are the technical conditions to get a complete fault detection? and • How could one guarantee full scope faults isolability? The study and considerations to solve the first task are the main contributions of this work. one may select analysis tools based on structure properties. u . In particular. Here one describes briefly the main tools of the SA. A system can be described by a bipartite graph G with its variables V and its equations C as node sets where there are edges connecting constraint with variables (Gross & Yellen. θ the parameter vector. f ). historical data. v j ) if and only if v j appers in ci ⎪ eij = ⎨ on the contrary ⎪0 ⎩ . or Bond Graph (Mukherjee et al. f ε ℜ f . to deal with large scale complex dynamic systems. with this approach. Linear Structured Systems (Dion et al. E) where the edges connecting set E is given by ⎧(ci . u . 1994). In particular. the generic structural approaches are more appropriated than the numerical methods. signal processing. f ). Since. and it can be used in the early design phase of a supervisory system. x . 5) is defined by the graph G = (C ∪ V.. For the GT of a combined cycle power plant. 2008).. The bipartite graph associated to Equations (3. 2006). x ε ℜs . allow to study the system capabilities to detect and isolate faults.. 2006). The number of feasible ARRs depends strongly on the measurements signals available and the sensors location and the structure of the plant under supervision. by a diagram or a binary incidence matrix. which is based on graph theory.θ . 2001). 2004). including the redundancy graph concept as an extension of the analytical redundancy relation used in the model-based fault diagnosis methods (Verde & Mina. u ε ℜnu . which have been proposed to achieve this goal. 2. to know if there are redundant variables in a system. f ).1 System description by a graph The Structural Analysis is based on relationships between variables given in the form of a bipartite graph or equivalently as an boolean incidence matrix. as Structural Analysis (Cassal et al. f . f and f faults to be detected and neglected respectively. etc. f .. This is the main reason to select SA for the GT fault issues in this work. u . Structural Analysis (SA) framework.θ . This framework has two relevant characteristics: allows dealing with complex and large scale systems and does not require numeric parameters information. 0 p ε ℜ p with u and y known variables. while the second task is focused on the selection of ARRs for specific fault sets. x . Definition 1: Let a dynamic system be given by x = f m ( x .Application of Structural Analysis to Improve Fault Diagnosis in a Gas Turbine 309 interval. the better performance could have the active diagnosis system.θ . x ε ℜn . Thus. only its structure without explicit numerical values plays an important role. 4. There are two form to shows the connection between nodes in a graph. the more variables are measured. f ε ℜd y = h( x . u ) x 2 = g 2 ( x1 ) y = g3 ( x2 ) (c1) (c2) (c3) In this simple case. where the exogenous set U and the measurements set Y have cardinality nu and ny respectively and then nk = |K| = nu + ny. • the constraints nodes set C = {c1. column j. To establish relations between the variables of V and the constraints of C. 1 where a shadowed circle denotes a constraint. . This is an advantage to study the system diagnosis capability. c3. as changes in the subset C or as an input node subset F without numerical values. 2008).5). The respective description incidence matrix. y. u. x2.310 Gas Turbines Using the matrix description an edge eij is given by • in row i. Example. E) allows to consider faults indifferently. the graph description G(C ∪ V. however not all can be used for fault detection analysis. d} where d corresponds to the constraint x1 = dx1 dt The bipartite graph is given in Fig. • the known variables set K = U ∪ Y. since the redundant relation between variables and the causality of a process have to be considered. This process in which each node ci is used to express only a node of V is called matching process. In the incidence matrix framework. The Structural Analysis. This is equivalent to define paths joining nodes of V with nodes of C. in the graph description. 2003).. c2. only matchings with redundant information are relevant. From fault detection point of view. the constraints nodes set C has cardinality |C| = 2n + ny + p and the variables nodes set V = Xg ∪ K ∪ F ∪ F is defined by • the unknown variables set Xg = X ∪ X ∪ X with cardinality 2n + s.4. There are diverse matching algorithms (Krysander et al. x1 }. • the fault and disturbance (neglected faults) sets F and F have cardinality f and d respectively.. is shown in Table 1. IM. SA deals with the systematic procedures to get the redundant relations from a bipartite graph without numerical value (Blanke et al. The symbols (• →) denotes initial node. Each state variable xi involves a constraint • xi = dxi dt (d) Since a fault f which changes the normal behavior of constraint ci means that the edges eij for any j are sensitive to f. consider the following simple differential algebraic system x 1 = g1 ( x 1 . the edges of E has to be oriented. (3. To show the simplicity to get a bipartite graph and the matching assignment. in which the symbol ⊕ in the row i and column j denotes that the constraint node i is used to get the variable node j. the matching process means rows and columns permutations. According to Eqs. • the variables nodes set is given V = {x1. Bipartite graph of system (c1. a real time comparison of û with the data of u detects any abnormal conditions involved in any of the constraints set (c1. ARR. c2.e. where ○ denotes concatenation. one matches x2. c3) and the difference ˆ r ( t ) = u − u = g1 d g 2 g3 ( y ) − u (7) is a symptom signal.y).Application of Structural Analysis to Improve Fault Diagnosis in a Gas Turbine 311 Fig. Incidence Matrix of the Bipartite Graph From matrix of Table 1.y) are known. one can estimate û by data of y and the path of evaluation. called residual signal r(t). 1.c3. The evaluation of (7). Therefore if the variables pair (u. one reaches x1 and later one. using x2 with c2. as second step. is zero in normal ideal condition and different from zero in abnormal conditions.d) \ c1 c2 c3 d x1 • • • x2 • • • x1 • u • y • Table 1. Path to evaluate u by y y •→ x2 ⊕ • x1 x1 u ⊕ • • ⊕ • →⊕ . the matching with initial node y shown in Table 2 is generated and the path is read as follow: using the constraints c3 together with the variable y. then it is a analytical redundant relation. by d the unknown variable x1 is determined and finally the goal node u can be evaluated by c1. − − − ˆ u = g1 1 ( d( g2 1 ( g3 1 ( y )))) (6) Thus. since the rest of variables has been before calculated.c2. since r(t)t only depends of the data pair (u. i. \ c3 c2 d c1 Table 2. the just-constrained G0 with the same number of constraints and unknown variables. the existence of ARRs or relations of class (2). 2008). This is equivalent to give an orientation to each edge.. the starting point of the faults structural analysis is the canonical Dulmage-Mendelsohn decomposition of the graph in three sub-graphs: the over-constrained G+ with more constraints than unknown variables Xg+. 3 unknown variables and the pair (u. Fig. The relations between variables set K+ with constraints C + in which the set Xg+ has been substituted. Since the paths from y to u o viceversa pass by all constraints (c3.y) as known nodes.. 2. 2 shows the generic structure of a decomposed graph in three subgraphs. 2003). eliminating the set Xg+ using some members of C +. determine the ARR’s. the involved constraints can be interpreted as operators from a set of known variables to others where the path is determined by a concatenation process following an oriented graph. The concatenation algorithm for linear constraints is reduced to the Mason’s method (Mason. the Dulmage-Medelsohn decomposition identifies the condition G+ = G with 4 constraints. 1956) and there are diverse ways to select the ARRs from the paths of a graph. c1). Once a matching is obtained in G+.d. Canonic Decomposition of a generic Incidence Matrix 2. the path of Table . Thus. c2. 1. Thus.2 Redundancy in a graph In the framework of Structural Analysis. actuator and constraints are generic detectable. faults which affect constraints involved in G0 and G− are not detectable (Blanke et al. and the under-constrained G− with less constraints than unknown variables. all faults associated to sensors.312 Gas Turbines Fig. Furthermore. For the particular graph G given in Fig. implies that the graph has more constraints than unknown variables and the maximum number of redundancy relations is bounded by |C|–|Xg|(Krysander et al. . members of Usi are independent variables which are correlated with yi by paths of the redundant graph. the redundant subgraph allows the determination of correlated variables without numerical values. 4. Usi . c2. From Table 2. Other graph can be built if u is the inicial node and y the target node. yi ) (9) is a Redundant Graph if • Paths between the vertices of Usi and the target yi are consistent and they can be obtained concatenating Ci without faults. One can build the faults symptoms (faults signature) from the RGi. (2008). Identify the subgraph G+. initial vertex of Usi and target vertex yi. without numeric values of a system model. Note that for an specific RG.Application of Structural Analysis to Improve Fault Diagnosis in a Gas Turbine 313 2 is a base to generate the ARRs for the model (c1. Eliminate the constraints set Ce which involves not invertible functions and build + Cinv = C+ \Ce. then RGi ( Ci .y. Step 3.u). 7 is a particular analytical redundant relation.3 Redundant graph definition Let Ki = Usi ∪ y i (8) be a subset of known variables matched with the subset of constraints Ci. Since both paths pass by the same nodes.d. 2.c3). In the matrix framework. there is a lack of consistency in some paths between Usi and Yi for any elements of the constraints set. 5) Step 1. faults which are unknown a priori are considered inconsistent vertices in the graph.c2. General advantages of the RGi are: • • One can generated distributed subgraphs where cause and effect can be indistinctly handled. • • 2. Eq. Step 2. For large scale systems. and At fault condition. symbols • → and → • are used for initial and target vertices respectively. then both are equivalent sets from redundant point of view. This has been used to isolate faults Mina et al. In this framework. This is useful to search new sensors which improve the faults signature. c1}. with y as initial node and u as target node. one identifies the path from y to u as a RG({c3.3. 1990). Calculate the canonical decomposition of G using only the unknown variables set X (Pothen & Fan.1 RG algorithm The following algorithm summarize the steps to get redundant graphs RGs assuming known the bipartite graph of the system (3. selecting ni nodes out of nk − 1. k13 MW x3 k3 k4 x9 k7 k1 k12 Stack x11 Start Motor Exciter Generator Vel k2 Compressor Combustion Chamber Gas Turbine HRSG k17 k5 x8 x10 x14 x6 x12 x1 x16 x15 k6 x17 x18 k11 k10 k14 x23 k15 x25 After Burners Valve AB k18 k9 Fig. otherwise continue. At ISO conditions. end the algorithm.314 Step 4. Initialize the number of initial node ni = 1 in the search and the number of assigned redundant graph nGR=0. this means ⎛ n − 1⎞ (nk − 1)! I = nk − 1Cni = ⎜ k ⎟= ni ⎠ (nk − 1 − ni )!( ni )! ⎝ for each target node + Step 7. Step 6. If ni = nk − 1. two heat recovery-steam generators and a steam turbine. electric generator EG. Step 9. 3. with nk the cardinality of set K. on the contrary ni = ni + 1 an return to step 6. Calculate the possible distinct combinations of the initial nodes for each target. if nGR = Maxrr. 3. and heat recovery HRSG. The main components of the GT shown in Fig. 3 are: compressor C. Bring up the number nGR according the assigned redundant graphs. end the algorithm. gas turbine section T. Calculate the possible maximal number of redundant graphs given by + Maxrr = Cinv − X + Gas Turbines Step 5. This model may go from cold startup to base load generation. Components of the Gas Turbine k8 k19 k9 x26 k16 . the ideal power delivered for each GT generates 80MW and the steam turbine 100MW. Step 8. Gas turbine description The GT behavior model used at this work simulates electrical power generation in a combined cycle power plant configuration with two GT. combustion chamber CC. Assign the orientations of the I graphs using the set Cinv for each target node including the cycle graphs (no diagonal submatrix) and constraints of the class d. k15 } (11) • with |Ys|=9. . 2010).. 1996) and it is integrated by nc = 28 constraints. avoiding an stall or surge phenomena. The process sensors is determined by the set Ys = {k1 . k18. k11 .additional combustion at heat recovery for increasing the exhaust gases temperature). The generic architecture and interconnection of the GT’s components are described by the block scheme given in Fig. k16}. 4. and the second one supplies gas fuel to heat-recovery afterburners (starting a second.Application of Structural Analysis to Improve Fault Diagnosis in a Gas Turbine 315 Fig. k9}. Also the GT unit has an actuator for the compressor inlet guide vanes. A generic compressor bleed valve extracts air from compressor during GT acceleration. k10 . the first supplies gas fuel to CC. k8. The dynamic nonlinear model is developed in (Delgadillo & Fuentes. IGVs. k2 . k7. and n = 9 dynamic-differential constraints. k19}. The variables and parameters for each block of the scheme are related by the constraints described in table 3. k4. and the control signals defines the set Uc = {k17. ns = 19 static algebraic constraints. the external physical variables determine the set Up = {k3. k13 . to get the required air flow to the combustion chamber. The variables are given in Appendix 8 and the description of the functions and parameters can be consulted in (Sánchez-Parra et al. 4. Gas Turbine Variables Interconnection The GT unit has two gas fuel control valves. the position transducers from actuators define the set Ya ={k5. k14 . 4. Analysis of the structure for the gas turbine Considering constraints and variables of the model described in Table (3) the following sets for the graph description are identified: • The set of known variables is given by K = Ys ∪ Ya ∪ Up ∪ Uc (10) with cardinality 19. Concerning the variables one can identify 27 unknown variables xi and 19 known variables ki. k6 . There are 28 physical parameters θi which are assumed constant in normal conditions Sánchez-Parra & Verde (2006). k12 . k1 . θ19 ) d3: 0 = x7 − dx6 dt c13: 0 = f ( x13 . k13 . k3 . θ14 . x17 . Then the constraints set has cardinality 37 and is given by C = {c 1. GT c14: 0 = f ( x10 . θ5 ) f ( k1 . θ18 . x10 . θ16 ) 0 = x24 − dx23 dt 0 = f ( x15 . GT Model Equations with the variables meaning given in the appendix • The constraints set is given by 19 static constraints and 9 state constraints which require their additional constraints (di) and known variables. k1 . k2 . x15 . x11 . θ0 ) 0 = f ( x25 . x12 . k5 . θ25 ) x5 − dk5 dt Gas Turbines Combustion Chamber Unit. k2 . θ12 . x22 . x24 . (14) the unknown variables set which are related by static relations of cardinality | X |=14 are . x6 . x15 . k3 . k2 . x23 . θ24 ) 0 = f ( x15 . x14 ) c10: 0 = f ( x6 . θ8 . x12 . θ1 . x20 . x8 . θ9 . k7 . x18 . k1 . k3 . k1 . k1 . x19 . x23 } . x17 . k4 .… . θ9 . k6 . k6. x14 . θ10 ) c19: 0 = f ( x19 . x26 . θ18 ) c15: 0 = f ( x1 . k14 . θ15 ) c22: 0 = f ( x20 . θ5 ) f ( x9 . k8 . k10 . k8 . x18 . θ17 . CC c8: 0 = f ( x6 . x8 . k13 . θ7 ) c9: 0 = f ( x10 . HR c23: c24: c25: c26: d7: c27: c28: d8: d9: 0 = f ( x23 . k10 . x23 . k1 . x7 . θ0 ) f ( x3 . k3 . k16 . θ10 ) c16: 0 = f ( x1 . x15 . θ9 . k1 . x10 ) f ( x5 . c 2. x9 . k11 . x12 . θ17 ) d2: 0 = x2 − dx1 dt c12: 0 = f ( x1 . k19 . k9 . x14 . k9 . k10 . x25 . k11 . k11 . k6 . θ26 ) d4: 0 = x13 − dk8 dt Heat Recovery Unit. C c1: c2: c3: c4: c5: c6: c7: d1: 0= 0= 0= 0= 0= 0= 0= 0= f ( x1 . k3 . x6 . θ8 . θ11 ) d5: 0 = x4 − dk2 dt c20: 0 = f ( x4 . k5 . x21 . θ22 ) d6: 0 = x21 − dx20 dt Table 3. θ13 . θ23 ) 0 = f ( x26 . x16 . k12 ) c18: 0 = f ( x6 . θ2 . x21 . c 28} ∪ {d1. k15 . θ18 . θ20 ) Electric Generator Unit EG c21: 0 = f ( x20 . k10 . k2 .… . x2 . x16 . θ16 . k18 . θ10 ) c17: 0 = f ( x6 . d 2. d 9} (12) • The unknown variables are 27 and define the set X = X ∪X ∪X (13) where the dynamic unknown variables set has cardinality 4 and is given by X = {x1 .316 Compressor Unit. k14 . k16 . x12 . k1 . k17 . k14 . k1 . k6 . k10 . x26 . θ4 . θ27 ) 0 = x22 − dk14 dt 0 = x27 − dk16 dt Gas Turbine Unit. . x16 . θ6 ) f ( x3 . θ21 ) c11: 0 = f ( x1 . θ19 ) 0 = f ( x27 . θ3 ) f ( x3 . x6 . x9 . 2008) the decomposed incidence matrix given in Fig. x19 . The unknown variables X 0 cannot be bypassed in any path and as consequence does not exist a RG. x11 . The third column indicates the variables used to detect faults involved in the respective set of constraints for each RG. the Incidence Matrix. exhaust gases enthalpy and combustion chamber gases enthalpy (x18. 4. x18 . Giampaolo (2003) calls this subsystem. the main concern of this section is the identification of the unknown variables. Table 4 is obtained and the failured components which can be detected in the GT are identified. Diagnosticability improvement in the GT The subsystem G0 given at the top of the matrix in Fig. The bottom sub-matrix IM+ ∈ I30×20 is associated to G+ and IM0 ∈ I7×7 for G0 with G− = Ø. it is impossible to detect a fault at the turbogenerator section with the assumed instrumentation. x 4 . The diagnosticability analysis of the first part of the analysis takes into account only the over-constrained G+.1 Graph structure modification The oriented graph of G0 assuming the known variables subset K is shown in Fig. x8 . 6 and concatenating these with other 10 constraints. The absence of paths which link a subset of known variables is recognized. 5 describes the process without redundant data and and the unique matched graph is shown in Fig.Application of Structural Analysis to Improve Fault Diagnosis in a Gas Turbine 317 X = {x3 . Considering the above described sets of variables and constraints. x10 . 5. 7. x13 . Considering the matching sequences described in the first 20 rows of Fig. 5. As example faults in the component of constraint c9 can be supervised by the graph RG7 or RG8 with different subsets of K. x2 . rotor acceleration x4 and the start motor power x11. 5 is obtained. x16 . x25 . IM. Using Matlab (MATLAB R2008. x14 . x16). So. x15 . 7. GT Thermodynamic Gas and includes the non-measured variables: compressor energy and rotor-friction energy (x8. The issue of the undetectability of the subgraph G0 will be addressed in Section 5. x12 . x7 . . which can be measured and converted to new known variables. the maximum number of RG is given by |C+| −|X+| = 10. with this the graph decomposition G0 will be empty and the getting of the respective ARR yields by the new measurement. x26 } (15) and the differential of the state variables are X = {x5. exhaust gases density x17. Table 4 is obtained and the failured components which can be detected in the GT are identified. One can see that some faults can be supervised using two RGs. x22 . x24 . It involves some of turbogenerator variables given in Table 3. x21 . of dimension (37 × 27) is first obtained and this is the start point of the structural analysis. x17 . x19). x27 } (16) with | X |= 9. Without redundant relations. Thus.1 Redundancy of the GT structure Based on the subgraph G+. Decomposed Incidence Matrix for the GT. 5.318 Gas Turbines Fig. where G0 and G+ are identified by blocks . c1 . c2 . k11 . k8 . c7 d4 . k12 k2 . k12 k5 . k11 . k9 . k9 . k4 . c2 . k3 . c25 . c26 Known variables K k1 . c10 . k9 . k6 . c5 . c18 d1 . c22 d7 . k3 . c8 . c9 . k15 . k10 . k7 k8 . c27 d2 . c1 . k5 . Matching for the GT to get 10GR . k7 . c24 . k12 . k3 . Redundant Graphs obtained from G+ Fig. c5 . c13 d9 . c21 . k6 k1 . k6 . c17 . k18 k16. k2 .Application of Structural Analysis to Improve Fault Diagnosis in a Gas Turbine 319 RG ’s RG 1 RG 2 RG 3 RG 4 RG 5 RG 6 RG 7 RG 8 RG 9 RG 10 Used Constraints C + c4 c17 . c10 . k3 . k19 k1 . c8 . c10 . k10 . k7 . k8 . k19 k1 . c23 . c6 . k12 k1 . k14 . k5 . k11 . k13 k1 . k9 . c17 . c12 . k11 . 6. c17 d6 . k14 . c25 . c17 d3 . k11 . k2 . c23 . c9 . c28 d8 . k16 Table 4. c11 . c6 . k16 . k12 . k10 . k7 . a change in the friction parameter Δθ11 = 2 in c19 of the turbogenerator non linear model has been simulated. x3. c8 . transforming the whole structure to an over-constrained graph. and allows the construction of the redundant graph described in Table 5. k8 . c 19 . x12. k10 . d5 . x11 became a new known variable. k20 } (18) and the set of constraints of the turbogenerator C ∗ = {c1 . any changes in the parameters and the functions involved in this set of constraints ˆ generates an inconsistent in the evaluation of the target node k . Thus. c 15 . To pass by c20 the only possibility is to asume that x11 is measurable. One verify that estimating first the set {x1. k5 . k20 = x11. Thus. c 16 . k6 . Subgraph G0 without redundant information To determine which variables of G0 could modify this lack of detectability. Then. In other words adding a dynamo-meter to the GT instrumentation.320 Gas Turbines Fig. c 14 . one can estimate x11 following the path. paths which satisfy the RG conditions assuming new sensors has to be builded.2 Simulation results To validate the obtained redundant relation. the relation ˆ r (t ) = k20 − k20 (17) can be used as to generate a residual and the respective ARR11 depends on the variables set K * = {k1 . c 5 . 20 5. k2 . it is feasible to assume that the start motor power x11 is known. This proposition changes the GT structure. from the incidence matrix of the Table 5 one can identify that variable x11 appears only in the constraint c20. k12 . On the other hand. x15} by subsets of K and C+. k9 . ˆ x10. c 3 . one has to search for paths between known variables which pass by the constraint c20. k11 . c 2 . k3 . c6 . c 10 . c 17 . The time evolution of the . there are not two different paths to evaluate it. Taking into account physical meaning of the set X0. c 20 } (19) Thus. 7. k13 . The fast response validates the detection system. any numerical value of the turbine model can be used.k10 → k6 → k1 → k1.k13 → ⊕ ⊕ • • • • • ⊕ ⊕ • • →⊕ Table 5. Note that during the analysis of the detection issue.k3 → k2. but not in the analysis. The study using the structural analysis allows to determine the GT’s monitoring and detection capacities with conventional sensors.x12 x1 x3 x15 k2 → k2 → k1. Residual generated by the new ARR11 detecting friction fault at 5000s residual (17) for a fault appearing at 5000s is shown in Fig. The values set is used for the implementation of the residual or ARR. giving generality to this result. 8. To eliminate such subsystem. 6. Matching Sequence of G0 to get Fault Detectability Fig. a . 8. Conclusions A fault detection analysis is presented focused on redundant information of a gas turbine in a CCCP model. From this analysis it is concluded the existence of a non-detectable fault subsystem.Application of Structural Analysis to Improve Fault Diagnosis in a Gas Turbine 321 C 0 X+ K x4 ⊕ x19 ⊕ x17 x16 x18 x8 k20 = x11 d5 c19 c15 c14 c16 c3 c20 x1 x10. (2004). G. This means. Man and Cybernetics-Part A: Systems and Humans 38(1): 197–206. (2008). A.. (2006). Åslund. Due to space limitation it is reported here results only for a mechanical fault in the friction parameter. Vol. Using the eleven RG obtained here. S. Isermann. The Fairmont Press.. (1996). & Yellen. Systems Science 20: 31–42. J. A.. J. Korbicz. W. P. (2001). Springer. (1990). Berlin.. & van der Woude. J. a diagnosis system could be designed integrating the residuals generator with a fault isolation logic which has to classify the faults. Dynamic modeling of a gas turbine in a combined cycle power plant. Cassal. C. IIE. J. Since all constraints are involved at least one time in the 10 RGs of Table 4 or in Eq. M.. The gas turbine handbook: principles and practice. Schreier. M. (1994). Lecture Notes in Control and Information Science 244. Generic propertie and control of linear structured systems: a survey. Kowalczuk. M. M. Document 5117. E. P. Lunze. IEEE Trans Aut. P. Ding. De-Persis.. Fault Diagnosis System. Automatica 26(2): 459–474.DGAPA-Universidad Nacional Autóoma de México. Springer. . T. Frank. J. Graph Theory and its applications. Delgadillo. Nonlinear Observers for Fault Detection and Isolation. Dion. (2003). Commault. A geometric approach to nonlinear fault detection and isolation. México. M. References Blanke. & Alcorta-Garcia. Automatica 39: 1125–1144. (2008). one can achieve a whole fault diagnosis for any set of parameters. Fault Diagnosis. pp. From these relations one identified that a diagnosis system can be designed for faults in sensors. eleven GT’s redundant relations or symptoms generation are obtained. Springer. & Nyberg. J. actuators and turbo-generator. P. J. in spanish. Vol. Germany. M. Koscielny. Springer. & Isidori. Considering the new set of known variables and using the structural analysis. 399–466. & Fuentes. 7. Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy. & Cholewa. IEEE Trans. 8. Acknowledgement The authors acknowledge the research support from the IN-7410. X. Z. C. J. & Declerck. Structural decomposition of large scale systems for the design of failure detection and identification procedure. CONACYT-101311 and Instituto de Investigaciones Eléctricas. (2006). (2003). J. J.322 Gas Turbines reasonable proposition is the measure of the GT’s start motor power. Staroswiecki. Frank. Taylor and Francis Group.. Giampaolo. 1. Gross. Kinnaert. R. Control 46-6: 853–866. (1999). Instituto de Investigaciones Eléctricas. M. (17). (2003). Krysander. Berlin.. E. & Staroswiecki. Model-based fault diagnosis techniques. An efficient algorithm for finding minimal over-constrained sub-systems for model based diagnosis. Springer. on Systems. M. Diagnosis and Fault Tolerant Control. Rengaswamyd.. pp. Verde. Math-Works. Rengaswamyd. Mina. S. Proceedings of the I. Computing the block triangular form of a sparse matrix. R. MATLAB R2008 (2008). Sánchez-Parra.08. Verde. R.. Feedback theory.Application of Structural Analysis to Improve Fault Diagnosis in a Gas Turbine 323 Mason. Inc. 960–966.. Venkatasubramanian.. part i: Quantitative model based methods. IFAC. ACC-08. & Mina. (2006).. R.. Taylor and Francis. R. Seoul. A review of process fault detection and diagnosis: Part i: Quantitative model based methods.. (2003a). 9. & Fan. & Verde. Verde. Sánchez-Parra. C. Yin. A review of process fault detection and diagnosis. E.further properties of signal flow graphs. J.. C. Pothen. S. F. Venkatasubramanian. M. A review of process fault detection and diagnosis: Part iii: Process history based methods. (1956). S. Computers and Chemical Engineering 27: 313–326. (2006). (2008). Pid based fault tolerant control for a gas turbine. Yin.. & Ortega. V. C. M. M. R. Simulation and Fault Identification. part ii: Qualitative model and search strategies. R. Mukherjee. Seattle. & Suarez. Computers and Chemical Engineering 27: 293–311. Rengaswamyd. V. (1990). A review of process fault detection and diagnosis: Part ii: Qualitative model and search strategies. Bond Graph in Modeling. USA. ASME 132(1-1): –. & Kavuri.. part iii: Process history based methods. Karmakar. D. Fault isolation with principal components structural models for a gas turbine. Korea. Sánchez-Parra. Massachuesetts. V. Principal components structured models for faults isolation. (2003b). S. V. Computers and Chemical Engineering 27: 293–346. & Kavuri. Appendix k1 k2 k3 k4 k5 k6 k7 k8 k9 Compressor discharge pressure Turbogenerador rotor speed Atmospheric pressure Outlet temperature Compressor IGV position Compressor air discharge temperature Compressor air bleed valve position Gas turbine fuel gas valve position Inlet fuel gas valves pressure x5 x6 x7 x8 x9 x10 x11 x12 x13 Compressor IGV position rate CC gas temperature CC gas rate temperature Compressor energy Compressor bleed air flow Compressor outlet air flow Starting motor power CC gas fuel flow GT fuel gas valve position rate ... & Kavuri. Natick. C. (2003c). (2008). Venkatasubramanian. R. C. R. American Control Conference-06. Toolbox Control Systems. & Kavuri. S. (2010). R. Artificial Intelligence 16: 303–324. Journal of Engineering for Gas Turbines and Power. Computers and Chemical Engineering 27: 326–346. Yin. & Kumar-Samantaray. J. Analytical redundancy for a gas turbine of a combined cycle power plant. R. A. Venkatasubramanian. Yin. J. A. A. Rengaswamyd... (2003d). Variables and Parameter Definition of the Gas Turbine Model .324 Gas Turbines k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20 x1 x2 x3 x4 θ11 Heat recovery pressure Exhaust gas temperature Blade path temperature (BPT) Electrical generator power output Heat recovery gas temperature Heat recovery gas outlet temperature Afterburner fuel gas valve position IGV control signal GT fuel gas valve control signal AB fuel gas valve control signal Starting motor power CC gas density CC gas rate density Compressor inlet air flow Turbogenerator rotor speed rate GT rotor friction parameter x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 θ4 θ20 CC inlet gas flow CC outlet gas flow CC gas enthalpy GT exhaust gas density GT exhaust gas enthalpy GT energy friction losses Electrical generator power angle Electrical generator power rate angle Heat recovery gas rate temperature Heat recovery gas density Heat recovery gas rate density Heat recovery outlet gas flow AB gas fuel flow AB fuel gas valve position rate Compressor air density GT rotor inertia Table 6. The existing models describing high-temperature oxidation and diffusion processes in MCrALY coatings use simple approximated empirical dependences (of power-or other type) [1-4] for oxide film mass or thickness variation with time. However the practical application of these models for long-time prediction is often difficult or impossible because of the lack of reliable model input parameter values. while the alloys used in practice are more complex. Natalya Mozhajskaya2. Oxidation (Al2O3 oxide film forming on the external coating surface) and Al diffusion both towards the oxide film border and into the basic alloy of a blade are the mass transfer processes which determine coating lifetime at the usual operating temperatures.or three-component alloys). In the present case a coating alloy containing 5 elements-nickel. Joseph-von-Fraunhofer Str. 7. A blade coatings lifetime of 25000 h is required in stationary gas turbines at operating temperatures from 900 to 1000 ºС making experimental lifetime assessment a very expensive and often a not practicable procedure. Iosif Krukov2 and Vladislav Kolarik3 1Institute 1.. Alexander Rybnikov2. Petersburg 3Fraunhofer-Institut für Chemische Technologie. and differential equations describing the oxide-forming element diffusion in the «oxide-coating-basic alloy» system [5. Zhelyabov Str. . chromium. Some data on element diffusion factors can be found in literature only for simple alloy compositions (two. yttrium – is to be investigated. Konstantin Tadlya1. Politechnicheskaya Str. 76327 Pfinztal 1Ukraine 2Russia 3Germany 2Polzunov Pavel Krukovsky1. aluminium. 6]. 03057 Kiev Central Boiler and Turbine Institute. Data on Al diffusion factor can be found in literature studying similar element composition. 194021 St. Introduction Modern power gas turbine blades are subject to high-temperature oxidation and are protected by metal coatings of MCrALY type.12 Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) of Engineering Thermophysics. 2a. A feasible and low-cost method of coating lifetime assessment is the calculation analysis (modeling) of mass transfer processes of basic oxideforming elements (in our case Al) over a long period of time. such as diffusion factors of an oxide-forming element. 24. but only for three-component NiCrAl alloy [7]. The major element retarding oxidation of a coating is aluminium (Al) whose percentage in a coating amounts to 6-12%. cobalt.. The construction (selection) of a mathematical model which gives the adequate description of major physical processes occurring in the system under consideration and determining coating life.1 together with the unknown model parameters determined in p. The diagram of the approach (Fig. The use of the model will allow for a more accurate long-term prediction of mass transfer processes and metal coating life at given lifetime criterion. the formation of a so-called interdiffusion zone between the coating and the base alloy. which have been described in [5. 4. The performance of short-term experimental studies in order to find regular trends of the oxide film and interdiffusion zone formation and determine Al concentration distributions in a coating and a basic metal (CE) at different times and temperatures (coated sample exposures in furnaces). Long-term prediction of mass transfer processes and coating life with the use of the proposed model in p.326 Gas Turbines It should be noted that the models. . Calculational and experimental approach The essence of the present approach is the choice of such a mass transfer model and a set of data which. which is.3. 2. So the use of a full calculation-experimental approach diagram based on the identified Pn(T) model parameters provides more accurate predictions. the intensity factor of aluminum segregation in the interdiffusion and other zones) using the solution of inverse problems of diffusion based on the experimental data on Al concentration distributions at different coated sample exposure times and temperatures in furnaces. 3. 2. 6]. This approach was used for the analysis of chromium mass transfer in a coating with the formation of chromium oxide and chromium diffusion into a basic alloy [8] except for the coating life analysis. enable one to obtain a more equivalent model based on the solution of inverse problems of diffusion (IPD).1) to mass transfer prediction is as follows: 1. which gives the proximity of CM and CE profiles by minimizing the F value. when combined. In that case mass transfer from the coating to the base alloy occurs through the interdiffusion zone and the Al accumulation here begins to play an important role. A simpler diagram of prediction is usually used (Fig. Generally the diagram can be applied for simple alloy compositions. This work offers to define model factors (effective Al diffusion factor. This model makes it possible to find the calculated Cm concentration (profiles) for Al in the coating-basic alloy system. The factors of its mathematical description become all the more uncertain. it may lead to insufficiently accurate predictions due to the uncertain P0(T) model parameters. The purpose of this work is to improve the existing model of mass transfer processes in MCrAlY-type metal coatings as well as the development and application of the calculationexperimental approach to coating life assessment based on the proposed models and the solution of inverse problems of diffusion. for instance.1): model + literature P0(T) model parameters = prediction. for a three-component alloy [5. 6] disregard the importance of a number of alloys peculiarities of Al transport from the coating to the base alloy. The approach based on the use of short-term experimental data for model factor determination followed by the application of this model for long-term predictive calculations is called here as a calculationexperimental approach. As for more complex compositions. The identification of the unknown Pn(T) model parameters from experiments based on the IPD solution. M ⎥ ⎣ ⎦ j =1 ⎪ ⎭ m 0. E ⎤ / m ⎪ ⎬ ∑ ⎢ j. Diagram of the calculation and experimental approach to mass transfer and life predictive of gas turbine blade coatings. Experiment In this connection the purpose of short-term researches was a study of kinetics of the oxide film formation on a coating surface. Thus the calculationexperimental approach manifests itself as a way of improving the accuracy of the results of calculations and prediction of the processes at hand by identifying the mathematical model parameters based on the experimental data on the process being studied. 2 Model. . The construction of the mathematical model required the performance of special works concerned with the study of the regularities of high-temperature material and coating behaviour during longterm exposures at high temperatures and the development of a physically valid model for coating life prediction.5 → min (1) This method of IPD solution is given in more detail in [8. 4 Prediction Fig.3) by means of IPD solution based on the available short-term experimental data. The calculation-experimental approach under consideration suggests a search (identification) for model parameters (p. 1. 3.Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 327 1 Experiment. structural changes in surfaces layers of coated heatresistant alloys. 9]. Then the experiment was continued till coating life expiration in order to confirm the validity of the proposed method. 3 Inverse Problem Solution. and the modeling of structural-phase changes in coatings and at isothermal ageing the duration of which was sufficient for model parameter identification. The IPD solution amounts to searching for such Pu (T) parameter values for which the quantity F ⎧ ⎪ = ⎨ ⎪ ⎩ 2 ⎫ ⎡C ( P (T ) ) − C j . St. The obtained images were processed by means of «VideoTest Structure» software («Video Test». 5000. 700. 1000 900. The samples were electropolated with Cu before preparation (cutting. 3. The coatings were applied on IN 738LC alloy samples by LPPS (Low Pressure Plasma Spray) method. 10000. The standards of both pure metals and compounds and known-composition alloys have been used for quantitative concentration evaluations of elements under consideration. 10000. The program of coated sample tests. The window size for the element analysis was 100 µm parallel and 3 µm perpendicular to the coating surface (100× 3 µm). the X-ray spectrum microanalysis of coating and basic metal layers was carried out every 2 to 10 µm and up to 250 µm deep. mechanical grinding and polishing) in order to preserve the oxide film which had formed on a coating surface after exposure in the furnace. 1000. 20000 Table 1. 1000. The samples of the same thickness and composition were obtained by cutting cylindrical bar (10 mm in diameter and 100 mm long) into pieces. µm 100 200 100 200 Base material IN 738 LC IN 738 LC Exposure temperature. The following parameters were measured on each sample with the use of digital metallography: thickness of an oxide film and all layers formed in a coating and adjacent basic metal layer as a result of isothermal exposure in air. 5000. the volume fraction of phases existing in an initial coating and formed during isothermal exposure. atomic number and characteristic radiant fluorescence effects were introduced by using special computer program. 700. 15000.2 X-ray spectrum microanalysis The X-ray spectrum microanalysis was carried out using MS46 «Camera» X-ray spectroscope analyzer. hr 100. The isothermal oxidation in air was carried out in laboratory muffle furnaces (LINN HIGH TERM LK 312-type) equipped with parameter control system (PID-controls) allowing to put the furnace into a specified mode and maintain the required temperature. X-ray spectrum microanalysis and X-ray diffraction analysis for studying the changes which had occurred in coatings.328 Gas Turbines The work investigated the degradation of two coatings with different aluminum content. 950. Petersburg. 950. 1000 Exposure time. 15000. 300. 20000 100. The corrections for absorption. Coating Ni30Co28Cr8AlY Ni30Co28Cr10AlY Coating thickness. . Initial samples and those after isothermal exposure were subjected to metallographic examination by optical microscopy.1 Metallographic examination The inverted microscope «Neophot 32» (Karl Zeiss Jena) with the «Baumer Coptronic» video camera was used for the micrographic examination. 3. The isothermal exposure times and temperatures are given in Table 1. оС 900. 300. Russia). The curve for aluminium concentration variation across the depth of a coating and basic metal layer was built after each exposure. To this end. Samples before etching and poorly etched were used for study. The amount of θ-Al2O3 reaches maximum after 100 hours and with further exposure the oxide starts to disappear as a result of its transformation into α-Al2O3. 2. This method makes it possible to identify in-situ the following oxide phases.1 Protective oxide film formation mechanism The mechanism of oxide film formation and growth on coating surfaces after long exposures at high temperatures in air or pure fuel combustion products was studied (Fig. 300 h 1000 h 5000 h 15000 h 3. The growth of α-Al2O3 and θ-Al2O3 at 950 ºС as a function of time is given in Fig. Both alumina phases on polished samples grow simultaneously in the first 50 hours and then the rate of θ-Al2O3 growth decreases and α-Al2O3 increases.4 Experimental results 3. Methods of polycrystalline sample structure examination were standard. 3. Germany.4 μm 7. The experimental set-up consists of an X-ray diffractometer and a high-temperature device with a programmable thermal controler. 950°C and 1000°C) up to 20000 hours.4. .4 μm 4.3 as intensity curves iz(t). The in-situ observation of the oxide film formation during the first 100 hours at 900 and 950 ºС showed the formation of α-Al2O3 and θ-Al2O3 oxides on the surface (see Table 2). Oxidation measurements were carried out on coating under isothermal conditions (900°C.2). Oxide film thickness on a coating surface depending on time of isothermal oxidation The measurement of oxide film thickness after different exposure times show that the change in oxide film thickness at the initial stage of formation does not fit to the power-type dependence at longer exposures. To follow the formation of each phase in time or as a function of temperature. To evaluate kinetic data on each of the reactions involved. A set of X-ray diffraction patterns with a defined time interval or temperature step was recorded in situ allowing for the identification of structural changes in the sample as a function of time or temperature. To determine residual stresses in the oxide film or basic metal.3 μm Fig. The studies of oxide film phase composition were performed by high-temperature X-ray diffraction method in order to find out the causes of the accelerated oxide film thickness growth at short exposures. the X-ray diffraction analysis was performed using a DRON-3M diffract meter in Cu Kα radiation with corresponding filters.1μm 12.Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 329 3.3 X-ray diffraction analysis The oxide film formation in the first 100 hours was studied in situ by high-temperature Xray diffraction by Fraunhofer Institute for Chemical Technology. In order to identify the oxide phase structures ex situ after long term exposures. To detect the thermal expansion of all phases simultaneously. Al2O3.Al)2O3 forms on the coating surface simultaneously with α.330 Gas Turbines Temperature. these data were corrected in the developed model by splitting the oxide film growth curve into two parts (the first one refers to the period of simultaneous existence of θAl2O3 and α. 3000 2500 α-Al2O3 950 C Intensity iz(t) [cps] 2000 1500 1000 α-Al2O3 900 C Θ-Al2O3 950 C 500 Θ-Al2O3 900 C 0 0 10 20 30 40 50 60 Time t. оС 900 950 1000 100 θ. The results of the investigations performed enabled to plot the variation of the oxide film phase composition with time and temperature (Fig.+ α-Al 2O3 θ. an oxide of complex composition of a spinel type (Co. Oxide film phase composition on Ni30Co28Cr10AlY and Ni30Co28Cr8AlY 200 µm thick protective coatings (the phase indications in brackets mean. hr 5000 α-Al 2O3 α-Al 2O3 α-Al 2O3 10000 α-Al 2O3 α-Al 2O3 (Me 3O4) α-Al 2O3 (Me 3O4) 20000 α-Al 2O3 (Me 3O4) α-Al 2O3. Diffraction peak intensities of α-Al2O3 and θ-Al2O3 on polished coatings with 8% Al at 900oC and 900oC. As is seen from Table2. .Al2O3 oxides and the second — to period of only α. 3. At long exposures (≥2•104 hours). [hr] 70 80 90 100 110 120 Fig.+ α-Al 2O3 α-Al 2O3 700 α-Al 2O3 α-Al 2O3 α-Al 2O3 Time. the oxide phase composition on coating with aluminum content over 8% (NiCoCr8alY (for instance) after exposures in this time interval presents mainly α.Al2O3).Ni)(Cr.4). Investigations using standard X-ray diffraction methods were performed in order to find out the oxide film growth mechanism in the range of 3•102 — 2•104 hours.Al2O3. Me 3O4 Table 2. Me 3O4 α-Al 2O3. that their amount did not exceed 5 %). Hereinafter. It has been established that the oxide film phase composition in this range depends on aluminum content. .Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 331 Ni30Co28Cr8AlY Ni30Co28Cr10AlY Temperature. α.Al2O3 + complex-composition oxide of a spinel type (Co. Both the coating and basic metal compositions and the exposure times and temperatures will naturally determine the structural changes. The investigations have shown that all the coatings in their initial phase composition represent a matrix with a facecentered cubic lattice — γ-solid solution (Ni.Al2O3) in a wide time range of exposures of Ni30Co28Cr8AlY and Ni30Co28 Cr10AlY coatings for the temperature interval from 900 to 1000ºС.Al2O3 corresponding to exposure time to 2•104 hours at all temperatures. These changes depend on both boundary conditions including environment composition and the thickness and composition of an oxide film forming during long exposures and the thickness of a coating layer. 4.Al2O3 + α. 3. The structural changes in coating and surface layers of a basic metal and the thickness of the depleted layer were studied by optical metallography and the distribution of elements in the coating and basic metal layers — by X-ray spectrum analysis. hr Fig.2 Kinetics of changes in coating structures The coating structural changes and the redistribution of elements between a coating and a basic metal can be observed during long isothermal exposures of the coated basic metal. The work investigated the coating depth-variation of the chemical composition and structure and the changes in the surface layer of a basic metal during long exposures in air simulating service conditions in the medium of pure fuel combustion products.Al)2O3 corresponding to exposure time over 2•104 at temperatures 950ºС and above. The basis for the development of methods of corrosion life modeling for these coatings was the existence of constant phase composition oxide (α. . С 1000 α− Al 2O 3 α -Al 2O 3 о 950 + Me 3O 4 900 θ− Al 2O 3 0 + α− Al 2O 3 500 1000 10000 20000 30000 Time. 2001).Co)Al which is uniformly distributed across the coating layer.Ni)(Cr. As is known. the β-phase presents a compensation reservoir for aluminum which is spent on the protective oxide film formation on a coating surface (Brady et al. Diagram of phase transformations in protective oxide film on Ni30Co28Cr8AlY and Ni30Co28Cr10AlY coating Three areas can be seen on the diagram: θ.Co)-Cr-based and a β-phase (Ni.4. α.Al2O3 corresponding to exposure time to 200 hours at all temperatures. In relation to this. phase composition and structure depend on coating and basic metal compositions. The X-ray spectroscopy microanalysis of aluminium distribution in the surface layers of coatings in the initial state and after long exposure at 900 to 1000ºС was performed. coating application technique and subsequent heat-treatment conditions.6. Al2O3 (protection scale) γ β γ γ+ β γ Al2O3 (initial) β M23C6 γ Interdiffusion zone γ + β Base – In738 Fig.5. 15 µm) and the phase composition a significantly different from that for basic metal γ + γ′ +carbides. The kinetics of a change in the volume fraction of the β-phase and aluminium concentration depending on exposure time and temperature can be seen from the curves in Fig. The diffusion zone for all the coatings had about the same width (a. It should be noted that the β-phase stabilization is observed in coatings of this composition. This microanalysis allowed to identify phases which had been found during metallographic study. 5.332 Gas Turbines After applying a coating and performing heat-treatments a diffusion zone is formed in the alloy. The phase composition of the layers is mainly retained and their thickness changes with exposure time and temperature variation.7 and 8. the phase transformation in a coating during its degradation at hightemperature exposure occurs in the direction (γ+β)→γ. The zone width. The changes in coating structure and phase composition depending on exposure time and temperature can be traced from the structures given in Fig. Microstructure of Ni30Co28Cr8AlY coating on IN738LC alloy after exposure for 1000 hours at 950oC (×300) During long-term exposures to high temperatures the coating structure changes due to the phase composition variation in its different zones followed by the formation of the characteristic layers. It has been established that each of the coatings investigated after long-term exposures shows a specific character of structural changes. The sizes of dealloyed and diffusion zones and special features of element . The characteristic structure of this coating after high temperature exposures is given in Fig. the volume fraction of the initial β-phase amount to 45% for the Ni30Co28 Cr8AlY coating and 62% for NiCo28Cr10AlY. 6. a sharp decrease in aluminium content is observed under the oxide film Al2O3 (51. The external coating surface is taken as the onset of counting and considered to be constant in these phase transformation diagrams. which corresponds to its content in the γ-phase.78%) up to 2. The change in Ni30Co28Cr8AlY coating on IN738LC alloy after different exposures at 900°C. During the exposures this phase amount decreases according to the curves shown in Fig. The diagrams of phase transformation proposed by Tamarin Jr.5 to 3. Thus.2%.8. (Tamarin. the decrease being less intensive for the coating with greater aluminium content (and |or larger thickness) determining the coating aluminum life. .7.Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 333 20000 hr 900оС 100 hr 700 hr 1000 hr 5000 hr 950оС 100 hr 300 hr 1000 hr 5000 hr 10000 hr 1000оС 100 hr 1000 hr 5000 hr 10000 hr 20000 hr Fig. In coatings of this composition. 2002) are very convenient for presentation of data on the coating phase composition variation with exposure time and temperature. 950°C and 1000°C distribution in these zones can be seen from the curves built in Fig. for the external dealloyed zone characteristic for all types of coatings. % 50 40 30 20 10 0 исходное 300 ч 700 ч 10000 ч 60 50 40 30 20 10 0 0 исходное 300 ч 700 ч 1000 ч 10000 ч 0 20 40 60 80 100 120 140 160 180 200 220 240 Distance. This zone is formed as a result of β-phase solution and aluminium consumption for the protective oxide film Al2O3 formation.basic metal». мкм Fig. 8. mkm 20 40 60 80 100 120 140 160 180 200 220 240 Distance. The β-NiAl volume fraction in the γ+β region after different duration of exposure at 950 °C As is seen from Fig. At the same time. significant temperature-dependent structural changes of a diffusion zone are observed at the interface «coating .% 40 14 12 10 8 6 4 2 0 0 50 100 150 200 250 300 350 400 Distance.9 and 10 the phase changes in external layers at high-temperature exposures are observed only due to the formation of an external depleted zone the width of which increases with increasing exposure time and temperature. % Ni30Co28Cr10AlY(200 мкм) 70 Volume fraction β-фазы. The studies performed have found out particular features of the diffusion zone formation . The Al concentration profile across a coating after isothermal oxidation at high temperatures for up to 10 000 hour Ni30Co28Cr8AlY(200 мкм) 70 60 Volume fraction β-фазы. мкм Fig. 7.334 Gas Turbines 60 50 300 hr 1000 hr 5000 hr 10000 hr Al concentration. Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 335 900oC, 10% Al, 100 mkm 0 Distance, мкм -50 -100 -150 γ+β γ2 γ + γ' -50 -100 -150 -200 γ+β γ+β γ2 γ + γ'+carbides -200 -250 -300 -350 γ + γ'+carbides γ + γ' 900 C o -250 -300 γ + γ' 950 C o 1000 900oC, 10% Al, 200 mkm γ+β 10000 γ1 -350 1000 950oC, 10% Al, 200 mkm γ1 10000 Distance, мкм 0 -50 -100 -150 -200 -250 -300 -350 1000 0 -50 γ+β -100 -150 950 C γ+β γ + γ'+carbides γ + γ' -200 -250 -300 γ+β γ + γ'+carbides γ + γ' Time, hr 10000 20000-350 1000 Time, hr 10000 Fig. 9. Diagram of phase transformations in Ni30Co28Cr10AlY coating on IN738LC superalloy after exposure at 900 °C and 950 °C between a metal and a coating depending on the aluminum content in the zone: with the aluminum content 10% the diffusion processes develop at the interface on a basic metal side (in this case a β+γ structure is formed), while with the aluminum content 8% in a coating the diffusion processes develop on both sides of the interface (the β+γ structure is first formed and then it transforms to a single -phase γ-zone). It is self-evident that the common model of the diffusion element redistribution in an oxide film, a coating and a basic metal requires accounting for the diffusion processes of all coating and alloy components. The practical handling the problem is however labour intensive, ambiguous, and requires a great number of experimental data. That is why there is a good reason to make a choice of the best concept of diffusion which could be used as the basis of a coating corrosion life prediction according to one or another dominant process depending on the temperature interval. In the temperature range 900 to 1000ºС it is advisable to use aluminum redistribution processes whose characteristics have been studied as dominant diffusion processes for building a model. Alloy Coating 900 C o o Alloy Coating γ1 0 950oC, 10% Al, 100 mkm γ1 336 Distance, мкм Gas Turbines 100 мкм 200 мкм 0 -50 -100 -150 -200 γ1 Distance, мкм 900 C γ+β o 0 -50 -100 -150 γ1 γ+β γ2 γ2 -250 -300 γ + γ' -200 -250 -300 -350 γ + γ' 1000 C Distance, мкм o -350 1000 10000 20000 Time, hr 0 -50 -100 -150 -200 -250 -300 γ + γ' Alloy Distance, мкм 800 1000 2000 4000 6000 800010000 γ1 Alloy Coating 0 -50 -100 -150 -200 -250 -300 -350 800 1000 2000 Time, hr γ1 γ+β 950 C γ+β γ2 o γ+β γ2 γ + γ' 950 C Distance, мкм o -350 1000 10000 Time, hr 4000 6000 8000 10000 0 -50 -100 -150 γ1 Distance, мкм 0 -50 -100 -150 -200 -250 -300 -350 800 1000 2000 γ1 γ+β γ+β γ2 -200 -250 -300 γ2 γ+β γ3 Alloy γ + γ' 1000 10000 γ + γ' 1000 C o -350 Time, hr 4000 6000 800010000 Time, hr Fig. 10. The phase composition transformations in Ni30Co28Cr8AlY coating (100μm and 200 μm on IN738LC superalloy after exposures at different temperatures (900 °C, 950 °C and 1000 °C). 4. Physical and mathematical models The physical model for aluminium diffusion redistribution in the «oxide-coating-basic metal»system obtained from the analysis of experimental studies of oxidation and diffusion processes in coatings of NiCoCrAlY-type is described as follows (Fig.11). An oxide is formed by combining aluminuim and oxygen which is absorbed from the gaseous medium and by means of diffusion through the oxide layer x1 — x0 it reaches the interface Coating Time, hr 1000 C o Coating Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 337 1. coating, 2. basic alloy, 3. γ -region, γ+ β region, 4. depletion zone, 5. interdiffusion zone Fig. 11. Typical aluminium concentration distribution in an oxide, coating, and basic alloy. x1 oxide - coating. The aluminuim diffusion from the coating proceeds in two directions: to the interface x1 oxide - coating where it enters into reaction with the arrived oxygen. to the interface x4 coating - basic alloy where it is accumulated in the interdiffusion zone and then diffuses to the basic alloy. The formation of aluminium-depleted single-phase zones with a decreased Al (γ-phase) content on both the oxide and basic metal side (depletion zones I and II, Fig.11) occurs at the cost of the aluminium departure from the coating (γ+β two phase zone. All aluminium leaving the coating departs from the coating (γ+β two phase zone owing to the β-phase disappearance. The aluminium concentration profile has the form of a stepwise curve in the region of NiCoCrAlY coating and a curve with maximum in the interdiffusion zone within the basic alloy. Six major zones can be distinguished: x0 < x < x1 oxide; aluminium-depleted x1 < x < x2 zone where only one γ -phase is present; two-phase x2 < x < x3 zone where γ - and β -phases exist simultaneously; x3 < x < x4 zone in the coating, also aluminium-depleted with γ -phase: interdiffusion aluminium-rich zone x4 < x < x5 in the basic alloy. x5 < x Zone in the basic metal where aluminium diffuses from the interdiffusion zone. The aluminium accumulation in the interdiffusion zone with time occurs at the cost of the formation of different phases (γ+β and γ’+β -phases, for instance) due to the different quantitative compositions and the corresponding thermodynamical equilibrium of elements in a coating and a basic alloy. The accumulated in the interdiffusion zone aluminium diffuses partly to the basic alloy and back to the coating. In the model under consideration, all the borders apart from the border x4 (the interface between a coating and a basic alloy) are movable. The borders x2 and x3 move toward each other because of the β -phase content decrease in the γ+β - two-phase coating zone x2 < x < x3 from which the aluminium diffusion occurs. The concentrations of total aluminium amount of C and β-phase Cβ in the γ+β twophase x2 < x < x3 decrease with time. A mathematical model presented in [6] was taken as the basis of the above-described model. The model from [6] was improved by adding the capabilities of accounting for special features of border x2 and x3 moving as well as the formation and growth of the interdiffusion zone which has a great effect on the aluminium mass transfer processes in the coating-basic alloy system. 338 Gas Turbines Below is given this improved model according to which aluminium mass transfer processes in the region of solution x1 < x < x∞ can be described by the main diffusion equation ∂ C ∂ τ x1 < x < x∞ , C = C ( x ,τ ) , x3 = x3 (τ ) , x5 = x5 (τ ) , at the initial condition = ∂ ⎡ ∂ C⎤ D +W ∂ x ⎢ ef ∂ x ⎥ ⎣ ⎦ Def = Def ( x ) , x1 = x1 (τ ) , (2) x2 = x2 (τ ) , τ > 0, , W = W ( x ,τ ) , ⎧ 0 ⎪C 0 < x < x4 C ( x, 0) = C ( x) = ⎨ п 0 ⎪C ос x ≥ x4 ⎩ at the boundary condition on border x∞ ∂C ( x∞ , τ ) ∂x =0 (3) (4) and boundary condition on the movable border x1 describing the aluminium diffusion flow from the coating to the left to form the oxide (Fig.11) at the cost of Al concentration gradient J оx ( x1+ ,τ ) = −Def ∂ C ( x1 ,τ ) ∂ x (5) dx1 that was formed owing to the border dτ movement to the right make up a total oxide film mass of ∆x thickness which can be described by two parabolic equation [5,6]. Flow (5) together with the mass (flow) C ( x1 ,τ ) ∗ ⎧ kоx ⋅ τ 0.5 , 0 < τ < τ * ⎪ Δx(τ ) = x1 (τ ) − x0 (τ ) = ⎨ ∗∗ ⎪ kоx ⋅ τ − τ 0 , τ * < τ < ∞ ⎩ (6), (7) ∗ ∗∗ where kоx , kоx - intensity factors of oxide film thickness growth, in literature often called oxidation constants, τ*- time prior to which the oxidation law (6) is valid and after which the oxidation law(6) is valid τ0 -time prior to which the oxidation law (7) is in force. At the moment of time τ* the curves from equations (6) and (7) cross; τ0 -the time (negative value) of crossing law (7) and the time axis τ. The necessity of describing the law of Al oxide growth by the two parabolic equations (6) and (7) is due to a more rapid growth of oxide θphase prior to the moment of time τ* and a slower growth of α- phase of the oxide film Al2O3 ∗ ∗∗ at τ > τ*. The factors kоx , kоx , τ0 and the τ* value in (6) and (7) are determined from the experimental data on the oxide film thickness growth with time. The border x1 movement is described by the equation k Al2O3 ρ Al2O3 1 dx1 = 0.5 1 ⎞ ρп dτ ⎛ τ ⎜1 + ⎟ s⎠ ⎝ Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 339 derived with regard to the stoichiometric relationship between Al and oxygen masses consumed to form an aluminium oxide. The relationship is used in the model of parabolic law of oxide film thickness growth (6.7). According to the accepted model prototype [6] the following concentration values are set on movable borders x2 and x3: C ( x2 − ,τ ) = C ( x3 + ,τ ) = Cγ , C ( x2 + ,τ ) = C ( x3 − ,τ ) = Cγ + β . (8) Then by analogy with the boundary condition (5) for a movable border x4 we can write the aluminium diffusion flow from a coating to the right to form the interdiffusion zone ∆y= x5 x4 and aluminium diffusion to a basic metal as J b ( x 4 − , τ ) = −Def ∂ C ( x 4 − ,τ ) ∂ x (9) In compliance with the physical model (Fig.2) the aluminium flow (9) arrived from the coating takes part in the formation of new phases in the interdiffusion zone ∆y= x5 - x4 thick and uniformly segregates in this zone , that is J b ( x 4 − ,τ ) = W ( x ,τ ) ⋅ Δy(τ ) (10) where the interdiffusion zone width ∆y= x5 - x4 increase with time due to the border x5 movement to the right and the parabolic law of its growth, as for the oxide film, is taken in the form of 0 Δy(τ ) = x5 (τ ) − x4 = kiz ⋅ τ − τ iz (11) 0 kiz factors and τ iz value in (11) are determined from the experimental data on the interdiffusion zone growth with time. The expression for Al W mass arrived from the coating and uniformly segregated in the interdiffusion zone x4 < x < x5 is taken as dependent on Cγ + β − Cγ . (in power m) and has the form ⎧ k ⋅ (Cγ + β − Cγ )m , x 4 < x < x 5 ⎪ W = W ( x ,τ ) = ⎨ w x1 < x < x 4 , x > x5 ⎪0, ⎩ (12) where kw -intensity factor of aluminium segregation in the interdiffusion zone. Since the balance of masses must be met in the coating-oxide film-basic alloy system the expression for the total aluminium flow departed from the coating two-phase zone, in accord with (5) and (9), will take the form J Σ (τ ) = J ox ( x1+ ,τ ) + J b ( x 4 − ,τ ) (13) In accord with the accepted physical model all aluminium flowing from the coating departs the coating γ+β two-phase zone at the cost of β-phase consumption. Then the movement of borders x2 and x3 as well as the aluminium concentration decrease in the γ+β two-phase zone can be described by the equation of mass balance between aluminium mass flows on these borders and the flows resulted from the aluminium concentration difference in γ+β - and γ phases ΔC = Cγ + β − Cγ 340 Gas Turbines J Σ = J γ ( x 2 − , τ ) + J γ ( x 3 + , τ ) = ΔC ⋅ where Jγ ( x2 − , τ ) = -Def dx2 dτ + ΔC ⋅ dx3 + ( x3 − x2 ) dτ dC γ +β dτ (14) dC( x3 + , τ ) dC ( x2 − , τ ) and Jγ ( x3 + , τ ) = - Def dx dx are diffusion flows to the oxide and basic alloy due to the aluminium concentration gradients to the left and to the right of borders x2 and x3 respectively. After division of all the terms by J∑ the expression (14) has form 1 = ΔC ⋅ dx2 dτ / JΣ + ΔC ⋅ dx3 / J Σ + ( x3 − x2 ) dτ dC γ + β dτ / JΣ = g2 + g3 + g2,3 (15) where g2 and g3 — total aluminium mass fractions gone from the coating due to the movement of borders x2 and x3 respectively, g2,3 = (1- g2 - g3) — a fraction of aluminium mass gone from the coating due to the Al β-phase amount decrease in the x2 < x < x3 zone. The g2 and g3 quantities having a direct effect on the rate of borders x2 and x3. movement are also taken as dependent on the concentration difference ΔC = Cγ + β − Cγ g2 = k2 ⋅ ΔC ΔC , g 3 = k3 ⋅ 0 0 Cп Cп (16) The laws of borders x2 and x3 movement and Al Cγ + β amount decrease in a two-phase zone can be derived from expressions (15) and (16) dx2 dτ = JΣ k2 dx3 , 0 C п dτ = JΣ k3 dCγ + β , = J Σ ( x 3 − x2 ) ( 1 − g2 − g3 ) 0 dτ Cп (17) The k2 and k3 coefficients of proportionality in (16) are determined from expressions (16) and (17) based on the experimental data on the dynamics of borders x2 and x3 movement and the value of platform Cγ + β in the region x2 < x < x3 for different sample exposure times. The association of total Al Cγ + β content with the β-phase C β (τ ) amount in the coating is described by the expression Al ⎡ ⎤ Cγ + β (τ ) = C β (τ ) ⋅ C β + ⎣ 1 − C β (τ )⎦ ⋅ Cγ (18) where Al C β = const is Al amount in β-phase. The diffusion factor Def, kw factor and the index of power m in the mathematical model (2) (18) are determined from the experimental data by solving the inverse problem of diffusion. The diffusion factor Def in (2) is valid for all the region of solution except for the subregion x2 < x < x3 where it was taken to be equal to a large value because of the lack of a space aluminium concentration gradient. The accumulated in the interdiffusion zone aluminium Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 341 diffuses partly back to the coating as a result of the aluminium concentration gradient to the right of the borders x4 The appearing here diffusion flow J iz ( x 4 + , τ ) = −Def ∂ C ( x 4 + ,τ ) ∂ x returns to the interdiffusion zone by adding to the main flow (9). The distinction of the above model from that in [6] is not only in the account for the interdiffusion zone but also in the introduction of total aluminium mass fractions g2 and g3 in (15) which departed the coating due to the movement of borders x2 and x3 This allow for a wider application of the model (2) -(18) to different coating compositions for which the rate of movement in not defined on the whole by concentration gradients on borders x2, x3 and x4. In term of the thermodynamic theory of diffusion, these borders can be determined by complex processes of the β and γ phase formation dissolution in a solid solution, but the practical application of this theory for complex systems under consideration is rather conjectural. Following assumptions are accepted in this model: the character of main physical-chemical processes occurring in the «coating-substrate» system does not change with time; only one element (Al) takes part in the formation of an oxide. This assumption for the coating type at hand is conformed by experimental investigations for up to 20000 hours the oxide forms on the border x1 only; aluminium comes to the interdiffusion zone only from a coating ; the diffusion factor Def derived by the IPD solution is an effective characteristic independent of time; the formation of new phases at the interface coating-basic alloy is not accounted for; no oxide film spallation takes place. The above formulated mathematical model of diffusion and oxidation processes is integrated by means of the numerical method of finite differences using the inexplicit diagram and iterative method of nonlinearity accounting. 5. Calculation results The application of calculation and experimental approach to the analysis of aluminium, oxidation and diffusion processes in a coating 100 µm thick is considered. The coating contains Ni35%, Co30%, Cr24% and Al8.4% (here and below the concentration is given in weight percents unless otherwise specified). The mathematical model (2) -(18) was used in calculations. The above described calculationexperimental approach was used for experimental conditions at 950ºС and exposures for 700, 10000 and 20000 hours. The model parameter identification was performed with the use of exposure for 700 and 10000 hours (Fig.12a, 12b). The results of Al and β-phase concentration distribution prediction were compared to the results of experimental exposure for 20000 hours (Fig.12b). The main input parameters in the model (2) -(18) were diffusion factors Def, intensity factor of aluminium segregation in the interdiffusion zone kw, the index of power m, weight parabolic equations(6,7) were found by the approximation of experimental data Δx ex = f (τ ) ∗ ∗∗ ∗ ∗∗ coefficients k2, k3 and coefficients kоx , kоx , and τ 0 . The coefficients kоx , kоx , and τ 0 in the 342 Gas Turbines Fig. Comparison of calculated and measured concentration profiles . 12. m = 0.phase disappearance in the coating for three temperatures 900.m2/s. kw =1.3⋅107 s.at T=950ºС.Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 343 ∗ for exposures 7000 and 10000 hours. The calculation results of the time of β. By using defined model parameters the corrosion lifetime of different coatings was assessed in comparison with the obtained experimental data (Fig. m = 0.at T=1000ºС.m2/s. Fig. The parameter values found by using the IPD solution were Def =7⋅10-16.65. kw =1.14.37⋅10-7 s-1 . The initial values of these factors were taken as follows: Def =1. Further operation of the coating with the dissolved β. The IPD solution was performed by the method described in more detail in [10]. In our case for the temperature 950ºС kоx = 2. 3 . which is impermissible.0%.13.44⋅10-10 m/s0.65 for all three temperatures in the experiments. the intensity factor of aluminium segregation in the interdiffusion zone kw and the index of power m were found by IPD solution. k3=0. It is commonly assumed that the time of a complete β.at T=900ºС . The diffusion factor Def. This criterion is determined by the fact that after the β. The index of power appeared to be constant m = 0.24. Β-phase C… (volume %) concentrations in a coating depending on time ….5. τ 0 =-3. 13. 22 thousand hours at 950ºС and 12. 1. Thus with the above criterion of coating lifetime in mind a lifetime of NiCoCrAlY-type coating with the initial Al amount 8.5. m/s оx The weight coefficients were preestimated from the analysis of experimental data k2=0.5 thousand hours at 1000ºС.0⋅10-15. 2.16.. 950 and 1000ºС are given in Fig.phase brings to the rapid oxidation of blade coating and basic alloy layers.5. Table3).0⋅10-8 s-1 . k ∗∗ = 7.88⋅10-9 0.phase disappearance the aluminium concentration in a coating is not sufficient for maintaining the protective oxide film formation.4% and 20µm thick is considered to be 50 thousand hours at 900ºС.phase dissolution is a NiCoCrAlYtype coating life. The Cγ value was taken from the experiment as equaling 3. .344 Gas Turbines ab- Ni30Co28Cr8AlY Ni30Co28Cr10AlY 200µm thickness on In738LC alloy.Calculated coating life (hour at temperature. Fig. 3 -on Table 3. 14. The results of different coating life calculations . 2 . 200µm thickness on IN738LC alloy. 0С 900 11400 49000 55000 46000 58000 52700 950 5000 12500 21000 28000 26000 34000 51400 980 20000 1000 1000 12000 8000 11500 22800 - 1 -coating (on alloy). The life of different coatings determined from the β-phase amount (volume %) versus time curves for coatings Coating (base alloy) Co29Cr6AlY (GS6K) Ni30Co28Cr8AlY (100 µm) (IN738 LC) Ni30Co28Cr8AlY (200 µm) (IN738 LC) Ni30Co28Cr10AlY (100 µm) Ni30Co28Cr10AlY (200 µm) (IN738 LC) Ni25Cr5Al2SiTaY ( CM 247 LC) Ni25Co17Cr10AlYRe (Rene80) Ni25Co17Cr10AlYRe (LPPS) (PWA1483 SX) Ni25Co17Cr10AlYRe (VPS) (PWA1483 SX) Calculated coating life time (h) at temperature. 1992. (SIEMENS. 1996. The existence of the interdiffusion zone was modeled and calculated and a more flexible approach to the calculation for two-phase border movement was introduced in the mathematic model as a result of model improvement. V. There is a good agreement between experimental and calculated aluminium concentration profiles and β. D. of Eng. . R. P.1996. The model taken from [6] was significantly improved.p. — p. 1989. Hagel. Condition and Life Management for Power Plants. I. Heckel. 32. M. p. Krukovsky. D.216. J. M. Kartavova. p. A. 18A. W. Numerical Modelling of High-Temperature Corrosion Processes/|| Oxidation of metals. in particular. . 250-257. .Y. 44.207. Kolarik. v116. 201. Biederman and K. The authors express their acknowledgement to the NATO Scientific Program. p. Interdiffusion in Ni-rich. Assesment of the thermal damage in the superalloy GTD — Baltika V. Nissleu D. №4. Lifetime Modelling of High Temperature Corrosion Processes. M. Krukovsky.|| Proceedings of an EFC Workshop.p. K. Kolomyteev. Ministry of Education and Science and the Institute of Engineering Thermal Physical. 231-245. Rybnikov. Modelling of Heat Transfer Processes in protective coatings of GT blades:|| Industrial Heat Engineering. Kryukov. p. N. p.Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (calculational and experimental approach) 345 6. 1998. Sims. M.. J.№6. 125137. — p.phase amount in a coating. edited by Ch. M. E. to Alperine S. D. 7. Nikitin. Ni-Cr-Al Alloys at 1100 and 1200ºС: Part II. E. 309-338. France)..: Metallurgy. of ASME. P. 1987. 23-30.p. Gaseous corrosion and strength of nickel alloys|| M. R. P. Cruse T. R. . For Gas Turbines and Power. to determine aluminium diffusion factor and perform rotating blade life predictions. Modelling the microstructural evolution of M-Cr-Al-Y coatings during high-temperature oxidation. Stamm W. — p.384. Meirer S. The application of the approach made it possible to evaluate model input parameters. Superalloys II. vol.. Thermal Barrier Coating Life Prediction Model Developed|| Trans. Nesbitt. Conclusions The proposed calculation and experimental approach has shown its efficiency in lifetime assessments of gas turbine blade coatings. Jues-Lorento. 2087-2094. A. P.: Metallurgy. p. 2001.: Metallurgy. J. Germany) for their participation in discussing the results of the work.p. Borggreen.p. Nesbitt. Inverse Problems of Heat Transfer (general engineering approach) — Kiev. 1987. M. Sisson. Tadlya.Trans. Lee. Auerkari. 1995. Stoloff. Book 2. p. 1984. Ukraine for the financial support of the researches. 19-39. 1.December. Krukovsky. N. (SNECMA. References P. —p. Metal heat-resistance calculation.|| Surface and coatings technology.218. p. K. Institute of Engineering Thermal Physics NaN Ukraine. Chartier.p. Diffusion coefficients and Predicted Concentration Profiles|| Met. Sheffer K. Tortorelli P. Protective coating for turbine blades|| ASM International. High-temperature oxidation and corrosion of intermetallic || Corrosion and environmental degradation. edited by M.247. Ch. II. Whright. Schutze|| v. J. 2002. . A. P. Hanrahan R. Materials Park. 2001 — p. Pint B.p.. ON. Tamarin Y. 229-311. 6.. F. p.346 Gas Turbines Brady M. . conducts to rotor from two sides and by the fans that are set up on the Retaining Ring. . The cooler air rotates in one close cycle. in this manner. 1. The air after cooling. cools with water flow. exits from the top of generator.13 Failure Investigation of Gas Turbine Generator Cooling Fan Blades by Experimental and Numerical Analysis Power & Water University of Technology (PWUT) Iran 1. Introduction In gas turbine power plants. a fan is used as a cooling system to dissipate generated heat in coils (copper conductors) and generator electric circuits at the end sides of its rotor. Ali Jahangiri Fig. Position and arrangement of blades and spacer pieces on Retaining Ring is shown in figure 2. The entrance and exit path of air for cooling has seen in this map. is blown in two sides of rotor. the air after passing from inside of rotor. and with passing from one cooler. the general map of generator has been shown in figure 1. Generator diagram At each of two sides of generator sets up 11 blades as an axial fan that separates with 11 spacer pieces. in order to identify the case of blade failure has been utilized (Hou et al. The face of two blade types is compared in figure 3. GEC-ALSTHOM replaced them by 14o angle of attack (without change in alloy type) in order to decrease the forces made to blades.348 Gas Turbines Fig. It must be noticed that all the failed blades had the 19o angle of attack and after failure. In some cases. . output power=118 MW. Cooling system equipments were supplied by GEC-ALSTHOM Belford under the following conditions. Arrangement of blades around Retaining Ring It is obvious that the fan blade has effective factors on the generator performance. A series of mechanical analysis and examination on a failed blade in gas turbine engine has been performed and nonlinear finite element to determine the stress of the blade. The fracture of cooling fan blades has been occurred five times at the turbine side of the generator in our case study. The review of pervious blade fracture analysis notes shows that it has been a serious problem in different types of blade. 2. just 10 hr after resuming operation following the last overhaul. fracture of blades can cause short circuit between rotor and stator and consequently generator explosion and lots of financial loss. Figure 3 defined the deference between angle and blades dimensions. but the height of them is same. 2002. 2000). Failure investigation of blade and disk in first stage compressor in an aero engine is done and Metallurgical examination and stress analysis revealed that the design shortcoming resulted in over-compensation of centrifugal bend moment and bad contact condition (Xi et al. Turbine rotation=3000 rpm. Beisheim & Sinclair. A width of 14o blades is lower than 19o.. 2002).. stresses and Vibration. On opening the turbine casing. Paris et al. 3. 2. Review of the history of the unit operation. cracked blades and uncracked blades.1 Visual inspection The statistical data revealed that all of these failures have happened in the first hour of operation after the first operation or repair of gas turbine. 1961-3). Deference between 2 types of blade in angle and their dimensions The efficacy of a fracture mechanics methodology to model the crack growth behaviour of fatigue nucleated cracks obtained under test conditions similar to those found in turbine engine blade attachments has been verified and Crack propagation lives has been calculated using stress results of FEM analysis (Hutson et al.Failure Investigation of Gas Turbine Generator Cooling Fan Blades by Experimental and Numerical Analysis 349 Fig. Review of the history of the blades repairs and/or modifications (change in blade angle of attack from 19º to 14º). Mechanical and experimental Investigation 2.. . 2005. Crack propagation trajectories under mixedmode conditions have obtained using the planner and maximum tangential stress crack extension criteria. Numerical analysis on14º and 19º blades: 1. 2. meaning that no fracture has happened after 100 hr of operation. Material and microstructure (quantometry).[fig 3] 2. Metallurgical examination of the fractures to identify the metallurgical mode of failure (SEM). Broken blades. CFD analysis in order to study the imposed stresses of the fan blades due to operation. Application of the finite element method for modal and harmonic analysis to calculation of the natural frequencies.. 4. 2005) the three dimensional fatigue crack in a typical military aircraft engine fan blade attachment by Franc3D has been simulated (Barlow & Chandra. three kinds of blades (for using 19º attack angle) were found. 3. In the following of these papers in this note we have performed two series of analyses and their results evaluated to identify the possible causes of failure: Mechanical and experimental Investigation as follows: 1. 2. (50Hz frequency of powerplant generators) dynamic stresses have been measured for any 14° and 19° blades. Comparison of these stresses with the limit stresses (presented in table 2) shows that the stresses imposed to the blade are much lower from this limit and therefore there is not possibility of blade failure in normal operation conditions. At 3000 rpm. Ultimate tensile stress σut 470 MPa Yield tensile stress σyp 325 MP Fatigue endurance limit σe 140 MPa Alloy Al 2024 Table 2.5 Cu 3.07 _ Si 0..07 _ Fe 0. However temperature rise in generator case was been higher and it was result of decreasing in sucked air flow rate for generator cooling (Poursaeidi & Salavatian. shaping and finally polishing of the blades surfaces. Crystals directed in the direction of the blade length are a proof of this production method. Dynamic stresses in the blade (Moussavi Torshizi et al. The failure site was in the transition radius between the blade airfoil and the blade base.350 Gas Turbines The failure was at the turbine side of the generator and there was no crack at exciter side. milling.97 4.6 Mg 1. Also result of metallurgical examination over blades shows that blades are not produced by die casting. Mechanical behaviors of aluminium 2024 are presented in table 2.6MPa 18MPa 10. 1990). Crack initiation point was at the centrally part of the airfoil on its concave surface.2 Material and microstructure Results obtained from the quantometry technique test that performed over blades show that the blade material is aluminum 2024 (table1). 2009.36 1. Some portion of the surface appeared black and pitted due to electric spark. Elements quantometry test Al 2024 Al Base Base Zn 0. 1993).Stress in 3000 rpm MPa 9 7. Blade number 1FE 2FE 3FE 4FE Max.11 _ Mn 0. But by changing attack angle of blades to 14º have not seen any failure.. Chemical composition of blade and its comparison with aluminium 2024 alloy (Joseph. Moussavi Torshizi et al.4 MPa Table 3. 2009) .67 0. Heat treatment performed in this blade is of the T351 heating operations (Moussavi Torshizi et al.. 2009).4 Table 1. (table 3). but rather molding. Mechanical strength of aluminium 2024 (ASM. 2009). theory of fatigue failure and dimple rupture is considered and for which one of the mechanisms. existing lines in fig 4(a) doubtlessly has been fatigue lines.Failure Investigation of Gas Turbine Generator Cooling Fan Blades by Experimental and Numerical Analysis 351 2. one surface with area 1cm×1cm is prepared so that for first mechanism is used of same damaged blades at powerplant generator. Because of microstructure change in failure surface. SEM could have been able to prepare best high quality picture of surface with highest accuracy (scaled to X1000). in the effect of oscillatory loading of blade. The faigue lines show that crack is initiated at one side and propagated in significant time. Therefore. crack is started from one or more point in the middle part of cave surface of wing (unsuitable quality of surface can be result of the start of crack) and is leaded to interruption of it . 2. is being failure surfaces study. (a) (b) Fig. gradual failure in the effect of endurance (fatigue) and / or failure in result of external material impact (Dimple Rupture). has employed Scaning Electron Microscope (SEM). and made progress in the time of turning. In order to study of failure surface and compare quality of these 2 possible failure mechanism with standard failure handbook of this alloy (AL2024) to recognise failure main cause. 2. In this section. While there is two possibility. there is no any resemblance between these 2 mechanism of failure and quality of surfaces is quietly differvaried. the wing is not interrupted in one moment in the effect of contact the external object.4 Survey of failure (scaled by SEM) surfaces With comparison between fig 4(a) and fig 4(b) that first is surface of broken blade at powerplant incident and second is broken in type of dimple rupture (breaking potholes) has been obviously seen. however cannot declare exactly the reason of the starting of the crack. This subsection engaged to inspection the failure surfaces and defining it's result. breaking incident and also for preparing surface by another mechanism a piece with this alloy is broken with only one knock of external object impact. This studies show that: 1.3 Study of fracture surfaces with SEM Its obvious that one of the most important ways to investigation of the failure pieces. (a) fatigue surface failure (scaled ×1330) (b) Dimple rupture result of instant impact (scaled ×2000) . 4. 3. creation weave centralization and the starting of crack of them is very probable. Fig. Therefore our purpose from CFD analysis is to achieve air velocity distribution around blades and also study of air flow lines (in order to observe probable vortex and related problems) and also determination of force resulted from air pressure over blades. To do this. Figure 5 has shown the final failure of surface and the ration of that to fatigue failure of surface as seen. 5. Vibration due to oscillatory change of pressure distribution in two sides of blade may cause blade fatigue. Comparison between final and fatigue failure surface 3. Computational Fluid Dynamic (CFD) code and Finite Element Method (FEM) were deployed to analysis stresses and vibration.352 Gas Turbines But the contact of hard particles to wing. entrance them in the surface. In this order after determination of blade profile (by using scanning digitiser camera ATOS1 (fig 6)) modelling air passage channel is necessary. Separation phenomena and turbulent flow (vortex formation) might be cause of vibration in fan’s blades. Numerical analysis on14o and 19o blades In order to study the imposed stresses of the fan blades due to operation. which was performed by CAD 1 One of the new and careful methods for acquiring solid profile by digital 3d photography . fan should be simulated. the most of surface is created with progress crack in the effect of periodically and fatigue loads. 6. 7. which generates the meshing for the volume. This file as a case file could be imported to CFD code (fig 8). Scanning digitiser camera Fig. Fig. is then imported to mesh generation software.Failure Investigation of Gas Turbine Generator Cooling Fan Blades by Experimental and Numerical Analysis 353 software (fig 7). The 3-dimentional model thus obtained. 3-dimentional model of blade and related passage channel . ∇ )V = − ∇P + ∇. Computational Fluid Dynamics (CFD) analysis 4.354 Gas Turbines Fig.2 Governing equations Because of the turbulence action induced by high Reynolds swirling flow pattern. 8 is divided into unstructured grids. The momentum equations is discretized by use first order upwind scheme. The pressure–velocity coupling is treated by SIMPLE algorithm. the pressure is discretized by using the standard scheme.V = 0 ⎛σ⎞ 1 (V. compressible fluid (air) and incompressible flow (because the Mach number is less than 0. 2003): ∇. the standard k-ε two-equation turbulence model is selected and the continuity and momentum that respectively describing mass and momentum can be written as follows (White. Above discretization methods can satisfy the accuracy require under such mesh size for this problem.4). The governing equations are solve under the boundary conditions described below by using he segregated method. Based on the finite volume method (FVM). Meshing domain in solution range 4.⎜ ⎟ − ρg + S ⎜ρ⎟ ρ ⎝ ⎠ (1) (2) The turbulence equations describing turbulent kinetic energy (k) and turbulent dissipation rate (ε) are as follows: .1 Discretization procedure The domain shown in Fig. 8. 4. "Steady state" was selected as solver and other conditions for flow and fluid are turbulent flow. ∇ )ε = ∇. which is a circle with a radius of approximately 70 cm.1592 rad s 4. Air pressure distribution over blades have also seen at these two figures. Tension result of this force is less than amount that solely causes to break the blade.1592 rad/s as calculated below).4 Analysis of flow field & pressure As see in fig.[(v + v t σ ε )∇ε ] + c 1ε ε ε2 P − c 2ε k k Here P is the generated kinetic energy of turbulence.p.m. The total volumetric flow of the cooling air is 45. (which will be approximately equal to ambient pressure) therefore “pressure outlet” is used. Solution convergence accuracy have been satisfied by iterating until residuals have decreased to minimum then result could have achieved and investigated.[(v + v t σ k )∇k ] + P − ε (V. it is possible to take a rotational component to axial velocity of air to count blade rotation (equivalent to 314. 4.3 Boundary conditions “Velocity inlet” is assumed as air entrance condition. = 50Hz 60 (5) (6) ω = 2π × fr = 2π × 50 = 314. is the difference between channel and generator shaft cross section): Q=V. 9 (a) & (b). For reduction of solution domain to reach to the least logical possible domain.225 m (Radius of shaft) Q= 45. In inlet duct cross section. velocity of air is calculated as follows (Also it should be in mind that area of air passage. It is observed the path lines completely tangent over the blades and the separation phenomenon has not incurred. Maximum absolute value of pressure that imposed to 19o angle of attack blade have reached to 56kPa on bottom of blade surface and then resultant force over the blade is approximately equal to 346N.∇ )k = ∇.6 m3/s Q 2 Then: V = = 16. in both blade type air flow pattern has been completely usual. the periodic analysis would be used. Also in 14o blade maximum pressure at the bottom of blade is reached to 39kPa that even is less than of 19o blade. In these kinds of problems that a moving object is the cause of fluid flow.6 m3/s for using 19o blade. fr = 3000r.Failure Investigation of Gas Turbine Generator Cooling Fan Blades by Experimental and Numerical Analysis 355 (3) (4) (V. and half of that is directed towards fan of turbine end and the other half is directed towards fan of exciter end.696 (Radius of air channel) r1= 0.A (7) r2= 0. .71 m/s A Because air pressure is uniform for all of the outlet area and along its duct. 9. (a) pressure Contour & velocity vectors passed over 19o angle of attack blade (b) pressure Contour & velocity vectors passed over 14o angle of attack blade .356 Gas Turbines Fig. In figure 10 and video No 1 displacement of both of blade tip at the first modal shape has shown. Modal analysis 2.8 2637.1 3879.4 these natural frequencies for fourth state in 2 blade types has been displayed. Wheras 19o blades is replaced with 14o blades the first natural frequency in fourth state (413. will not also move.1 Mode Shape Number Mode No 1 Mode No 2 Mode No 3 Mode No 4 Mode No 5 Table 4. This state has been selected for finite element harmonic numerical simulation. 4. All the points around the bolts are fixed. With respect to the fact that the first natural frequency of the 19o angle of attack blade in the fourth state (538 Hz) was very close (almost with 2% relative difference) to the frequency of the exciting force caused by shaft rotation (11 blades × 50 rad/s = 550 Hz) and therefore the incurrence of resonance in above conditions is very probable.49 Hz) will not be close (with 33% relative difference) to exciting frequency and therefore resonance condition will not occurred. the finite element method. the amount of bolts tightening was modeled and its influence on blade natural frequency was studied. Harmonic analysis The modal analysis on natural frequency and the harmonic analysis based on different excitation frequencies were done. 2. 5.5 Natural Frequency (Hz) 14o blade 413. In addition to all the points of the same height with bolts which are fixed.1 Modal analysis First.5 3837. All the points of the same height with bolts are fixed. 5.8 2693. The natural frequency in the 5 modes for these four states were calculated. was used to blade modelling and two analysis have been performed by finite element method: 1. four different states were investigated for both of 19o and 14o blade: 1. 3. which are in contact with the retaining ring. these forces caused by air flow are not enough to cause the blade rupture. To evaluate these conditions. In table. the elements. Finite Element Method Analysis (FEM) In order to determine the stresses acted on the blade and survey of the possibility of its failure caused by resonance.6 2365.9 2794. The whole blade root is fixed in all directions. Calculated natural frequency in the 5 modes for 19o and 14o blade .88 1339.49 1232.Failure Investigation of Gas Turbine Generator Cooling Fan Blades by Experimental and Numerical Analysis 357 While 19o angle of attack blade has been changed with 14o blade amount of force imposed to blade would decreased about 20% and is reached from 346 to 276N then. Natural Frequency (Hz) 19o blade 537. 1 Harmonic analysis for 19o blade From CFD analysis force acted by air flow on 19o blade was calculated about 346N. 10. 5. . Blade tip displacement for these conditions is shown in figure 11. domain. increases step by step.2.358 Gas Turbines Fig. the frequency of external forces (air flow and shaft rotating force) acted to blades. blade tip oscillation domain (blade tip displacement). (a) blade tip displacement at the first modal shape for 19o angle of attack blade (b) blade tip displacement at the first modal shape for 14o angle of attack blade 5. account for various frequences.2 Harmonic analysis In harmonic analysis. (from zero to 1000Hz) then. is accounted. By acting these external forces to blade in the various frequencies (between 0 to 1000 Hz). changing in blade type. difference shapes of vibrations and tension result of these acting external forces with. 11.Failure Investigation of Gas Turbine Generator Cooling Fan Blades by Experimental and Numerical Analysis 359 Fig. 12. 19oBlade tip displacement at various frequencies in first mode of vibration Fig. Contour of computed Von Mises tension exerted on 19oBlade at 550Hz frequency . 2 Harmonic analysis for 14o blade From CFD analysis force acted by air flow on 14o blade was calculated about 276. when the blade has been excited with 550Hz frequency. namely. 14oBlade tip displacement at various frequencies in first mode of vibration . blade tip displacement.49Hz). As seen. in 50Hz frequency blade tip displacement is reached to about 82µm this value grows with increasing frequency to the extent of 425 to 450 Hz reached to 220 to 280 µm. 13. is accounted. The blade will been vibrated intensely in this condition and as seen in fig 12. 5. the blade tip displacement again decreases intensely. blade material could be able to endure any forced statistical loads even at resonance state. that is near to first natural frequency. But thence that maximum amount of von mises tension is larger (68%) than fatigue endurance limit (236MPa > 140MPa) therefore. when blade is been encountered to fatigue condition at resonance condition. Blade tip displacement for these conditions is shown in figure 13.360 Gas Turbines As seen.8mm and hereafter by frequency increasing. By acting these external forces to blade in the various frequencies (between 0 to 800 Hz). Von Mises tension at sensitive spaces of blade (bade root) is reached to 236MPa.2. With notice to figure 11 resonance condition happening will be imminent. In first Natural frequency vicinity. By referral to table 2 is been obvious that tension with amount of 236Mpa is far less than any mechanical strength of alloy except fatigue endurance limit. This amount of displacement (4mm) has been even more than of 19o blade at vicinity of its first natural frequency (1. displacement is increased intensely and is reached to about 1. in 420Hz frequency blade tip displacement is reached to about maximum quantity (4mm) because of this reality that 420Hz frequency is nearest value to first natural frequency of 14o blade (413. 19o blade couldn’t be able to endure fatigue condition infinitely and blade fracture will be unavoidable.8mm).5N. Fig. With respect to the obtained results. Conclusion 1. Experimental study of ruptured surfaces shows that the probability of a collision of a large external object and its instantaneous rupture is impossible. 6. The blade will been vibrated intensely in this condition and as seen in fig 14. CFD analysis shows that the forces caused by air flow are not enough to cause the blade rupture. Contour of computed Von Mises tension exerted on 19oBlade at 550Hz frequency But as seen in fig 13. that is frequency of the exciting force caused by shaft rotation. when the blade has been excited with 550Hz frequency. Von Mises tension at sensitive spaces of blade (bade root) is reached to 388MPa. this analysis shows that the value of normal stress in most of conditions for 19 & 14o blades is about 10 MPa except in resonance state. 3. 14. 2. Fig.Failure Investigation of Gas Turbine Generator Cooling Fan Blades by Experimental and Numerical Analysis 361 With notice to figure 13 in 420Hz frequency resonance condition happening will be imminent. So again when 14o blade is been encountered to fatigue condition at resonance condition. Therefore in this condition resonance state will not been happened and Von Mises tension encountered to 14o blade root will be less than 10MPa that is so small to comprised. . 14o blade tip displacement will be less than 160µm. couldn’t be able to endure fatigue condition infinitely and blade fracture will be unavoidable. Blade failure will never been occurred for 14o blade in this condition. R. Properties and Selection. 23. Houston. In the case of applying a force with a frequency of nearby 550 Hz. (1963). 6. Int J Fatigue. Amsterdam Biner. early after operation (less than 100 h) and after the first operation or repair. G. Sih. resonance condition is probable) and because of applying stress at range of 160– 236 MPa cyclically and exceeds the endurance limit of the material. Shivakumar. Iran Power Plant Repair Co. and the point that if the element has not broken early after operation and has continued its usual work obtained results from CFD and vibration analysis.B. USA Barlow. Nonferrous Alloys and Special-Purpose Materials. NASA/FLAGRO. and the author would like to acknowledge the energy department of Power & Water University of Technology (PWUT) for their kind cooperation. (2003) Forman. 8. (1994). 7. Concerning the large number of turbines and regarding to this point that fracture happened in five case. In the case of applying a force with a frequency of nearby 550 Hz.G.B. (2001). Fatigue crack propagation simulation in an aircraft engine fan blade attachment.. Johnson Space Center..r. Power & Water University of Technology. 5.J. USA Alsthom Company report in conjunction with someone Gas Power Plant (1997) ASM. ASME. J. Blade failure will never been occurred. Semnan University). F. Colorado. VOL 2. Fatigue crack growth computer program.. 14o blade will not be exposed to a resonance condition and because of applying stress at limit of 10MPa. K. & Sinclair. FRANC3D Menu & Dialog Reference V2. 19o blade will be exposed to a resonance frequency (As a result. for their keen interest and encouragement for undertaking these studies. it will reduce working life of the blade and lead to failure after a number of cycle.C. & Chandra. (1990)..L. (2004) Failure analysis report of Iran-Neyshabour unit2B. Proceedings of ASME Turbo Expo. On the three-dimensional finite element analysis of dovetail attachment. Iran.W. Cornell University . Iran Power Plant Repair Co. the most probable reason for breakage phenomenon is the way blades have been fastened (how fixed are bolts). J. (1661-1668) Beisheim.2. Iran Power Plant Repair Co. 0-87170-378-5. References Anderson. On the crack extension in plates under plane loading and transverse shear. CRC Press. (519–527) Failure analysis report of Iran-Montazer-Ghaem unit6. (2002). J Basic Engng – Trans ASME.362 Gas Turbines 4. 85.c. (1995). R. with unsuitable blade fastening of the blade. Texas. (2002). 27. 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